LMFDB - Embedded newform 45.4.l.a.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0388957 + 0.145161i) q^{2} +(-5.17295 + 0.490448i) q^{3} +(6.90864 - 3.98871i) q^{4} +(9.52728 + 5.85072i) q^{5} +(-0.272400 - 0.731834i) q^{6} +(17.2584 - 4.62436i) q^{7} +(1.69784 + 1.69784i) q^{8} +(26.5189 - 5.07413i) q^{9} +O(q^{10})$	\(q+(0.0388957 + 0.145161i) q^{2} +(-5.17295 + 0.490448i) q^{3} +(6.90864 - 3.98871i) q^{4} +(9.52728 + 5.85072i) q^{5} +(-0.272400 - 0.731834i) q^{6} +(17.2584 - 4.62436i) q^{7} +(1.69784 + 1.69784i) q^{8} +(26.5189 - 5.07413i) q^{9} +(-0.478726 + 1.61056i) q^{10} +(21.0551 + 12.1562i) q^{11} +(-33.7818 + 24.0217i) q^{12} +(-51.6112 - 13.8292i) q^{13} +(1.34255 + 2.32537i) q^{14} +(-52.1537 - 25.5929i) q^{15} +(31.7292 - 54.9567i) q^{16} +(-62.6342 + 62.6342i) q^{17} +(1.76804 + 3.65215i) q^{18} -42.2427i q^{19} +(89.1574 + 2.41905i) q^{20} +(-87.0087 + 32.3859i) q^{21} +(-0.945647 + 3.52920i) q^{22} +(11.5350 - 43.0493i) q^{23} +(-9.61557 - 7.95016i) q^{24} +(56.5380 + 111.483i) q^{25} -8.02983i q^{26} +(-134.693 + 39.2544i) q^{27} +(100.787 - 100.787i) q^{28} +(-94.1659 + 163.100i) q^{29} +(1.68653 - 8.56613i) q^{30} +(-123.300 - 213.562i) q^{31} +(27.7661 + 7.43989i) q^{32} +(-114.879 - 52.5569i) q^{33} +(-11.5282 - 6.65583i) q^{34} +(191.481 + 56.9163i) q^{35} +(162.971 - 140.832i) q^{36} +(127.895 + 127.895i) q^{37} +(6.13199 - 1.64306i) q^{38} +(273.765 + 46.2251i) q^{39} +(6.24221 + 26.1094i) q^{40} +(-32.7974 + 18.9356i) q^{41} +(-8.08544 - 11.3706i) q^{42} +(35.1611 + 131.223i) q^{43} +193.950 q^{44} +(282.340 + 106.812i) q^{45} +6.69773 q^{46} +(-71.4005 - 266.470i) q^{47} +(-137.181 + 299.850i) q^{48} +(-20.5808 + 11.8823i) q^{49} +(-13.9839 + 12.5433i) q^{50} +(293.285 - 354.723i) q^{51} +(-411.724 + 110.321i) q^{52} +(-509.361 - 509.361i) q^{53} +(-10.9372 - 18.0253i) q^{54} +(129.475 + 239.003i) q^{55} +(37.1534 + 21.4505i) q^{56} +(20.7179 + 218.520i) q^{57} +(-27.3384 - 7.32531i) q^{58} +(-218.555 - 378.548i) q^{59} +(-462.394 + 31.2135i) q^{60} +(-438.507 + 759.517i) q^{61} +(26.2051 - 26.2051i) q^{62} +(434.208 - 210.204i) q^{63} -503.348i q^{64} +(-410.804 - 433.718i) q^{65} +(3.16090 - 18.7202i) q^{66} +(-92.9184 + 346.776i) q^{67} +(-182.888 + 682.547i) q^{68} +(-38.5567 + 228.349i) q^{69} +(-0.814223 + 30.0093i) q^{70} +534.313i q^{71} +(53.6400 + 36.4099i) q^{72} +(579.639 - 579.639i) q^{73} +(-13.5907 + 23.5399i) q^{74} +(-347.145 - 548.967i) q^{75} +(-168.494 - 291.840i) q^{76} +(419.591 + 112.429i) q^{77} +(3.93822 + 41.5379i) q^{78} +(522.214 + 301.501i) q^{79} +(623.830 - 337.948i) q^{80} +(677.506 - 269.121i) q^{81} +(-4.02439 - 4.02439i) q^{82} +(-58.9790 + 15.8034i) q^{83} +(-471.934 + 570.795i) q^{84} +(-963.189 + 230.278i) q^{85} +(-17.6808 + 10.2080i) q^{86} +(407.124 - 889.893i) q^{87} +(15.1090 + 56.3875i) q^{88} -858.746 q^{89} +(-4.52311 + 45.1393i) q^{90} -954.676 q^{91} +(-92.0196 - 343.422i) q^{92} +(742.569 + 1044.28i) q^{93} +(35.9039 - 20.7291i) q^{94} +(247.151 - 402.458i) q^{95} +(-147.281 - 24.8684i) q^{96} +(1300.14 - 348.372i) q^{97} +(-2.52535 - 2.52535i) q^{98} +(620.041 + 215.532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0388957	+	0.145161i	0.0137517	+	0.0513221i	0.972461	−	0.233067i	$-0.0748760\pi$
$2$	0.0388957	+	0.145161i	0.0137517	+	0.0513221i	−0.958709	+	0.284389i	$0.908209\pi$
$3$	−5.17295	+	0.490448i	−0.995536	+	0.0943868i
$3$	−5.17295	+	0.490448i	−0.995536	+	0.0943868i
$4$	6.90864	−	3.98871i	0.863581	−	0.498588i
$5$	9.52728	+	5.85072i	0.852146	+	0.523305i
$5$	9.52728	+	5.85072i	0.852146	+	0.523305i
$6$	−0.272400	−	0.731834i	−0.0185345	−	0.0497950i
$7$	17.2584	−	4.62436i	0.931863	−	0.249692i	0.239214	−	0.970967i	$-0.423110\pi$
$7$	17.2584	−	4.62436i	0.931863	−	0.249692i	0.692649	+	0.721275i	$0.256443\pi$
$8$	1.69784	+	1.69784i	0.0750347	+	0.0750347i
$9$	26.5189	−	5.07413i	0.982182	−	0.187931i
$10$	−0.478726	+	1.61056i	−0.0151386	+	0.0509303i
$11$	21.0551	+	12.1562i	0.577123	+	0.333202i	0.759989	−	0.649936i	$-0.225204\pi$
$11$	21.0551	+	12.1562i	0.577123	+	0.333202i	−0.182866	+	0.983138i	$0.558537\pi$
$12$	−33.7818	+	24.0217i	−0.812665	+	0.577873i
$13$	−51.6112	−	13.8292i	−1.10111	−	0.295041i	−0.337891	−	0.941185i	$-0.609714\pi$
$13$	−51.6112	−	13.8292i	−1.10111	−	0.295041i	−0.763215	+	0.646145i	$0.776380\pi$
$14$	1.34255	+	2.32537i	0.0256294	+	0.0443915i
$15$	−52.1537	−	25.5929i	−0.897734	−	0.440537i
$16$	31.7292	−	54.9567i	0.495769	−	0.858698i
$17$	−62.6342	+	62.6342i	−0.893590	+	0.893590i	−0.994859	−	0.101269i	$-0.967710\pi$
$17$	−62.6342	+	62.6342i	−0.893590	+	0.893590i	0.101269	+	0.994859i	$0.467710\pi$
$18$	1.76804	+	3.65215i	0.0231517	+	0.0478233i
$19$		−	42.2427i		−	0.510061i	−0.966933	−	0.255030i	$-0.917915\pi$
$19$		−	42.2427i		−	0.510061i	0.966933	−	0.255030i	$-0.0820854\pi$
$20$	89.1574	+	2.41905i	0.996810	+	0.0270458i
$21$	−87.0087	+	32.3859i	−0.904135	+	0.336533i
$22$	−0.945647	+	3.52920i	−0.00916421	+	0.0342013i
$23$	11.5350	−	43.0493i	0.104575	−	0.390278i	−0.893722	−	0.448621i	$-0.851915\pi$
$23$	11.5350	−	43.0493i	0.104575	−	0.390278i	0.998297	+	0.0583434i	$0.0185818\pi$
$24$	−9.61557	−	7.95016i	−0.0817820	−	0.0676175i
$25$	56.5380	+	111.483i	0.452304	+	0.891864i
$26$		−	8.02983i		−	0.0605684i
$27$	−134.693	+	39.2544i	−0.960059	+	0.279797i
$28$	100.787	−	100.787i	0.680245	−	0.680245i
$29$	−94.1659	+	163.100i	−0.602972	+	1.04438i	0.389397	+	0.921070i	$0.372683\pi$
$29$	−94.1659	+	163.100i	−0.602972	+	1.04438i	−0.992369	+	0.123307i	$0.960650\pi$
$30$	1.68653	−	8.56613i	0.0102639	−	0.0521318i
$31$	−123.300	−	213.562i	−0.714368	−	1.23732i	−0.963203	−	0.268775i	$-0.913381\pi$
$31$	−123.300	−	213.562i	−0.714368	−	1.23732i	0.248835	−	0.968546i	$-0.419952\pi$
$32$	27.7661	+	7.43989i	0.153387	+	0.0411000i
$33$	−114.879	−	52.5569i	−0.605997	−	0.277242i
$34$	−11.5282	−	6.65583i	−0.0581493	−	0.0335725i
$35$	191.481	+	56.9163i	0.924748	+	0.274874i
$36$	162.971	−	140.832i	0.754493	−	0.651998i
$37$	127.895	+	127.895i	0.568264	+	0.568264i	0.931642	−	0.363378i	$-0.118377\pi$
$37$	127.895	+	127.895i	0.568264	+	0.568264i	−0.363378	+	0.931642i	$0.618377\pi$
$38$	6.13199	−	1.64306i	0.0261774	−	0.00701421i
$39$	273.765	+	46.2251i	1.12404	+	0.189793i
$40$	6.24221	+	26.1094i	0.0246745	+	0.103207i
$41$	−32.7974	+	18.9356i	−0.124929	+	0.0721279i	−0.561162	−	0.827706i	$-0.689646\pi$
$41$	−32.7974	+	18.9356i	−0.124929	+	0.0721279i	0.436233	+	0.899834i	$0.356312\pi$
$42$	−8.08544	−	11.3706i	−0.0297050	−	0.0417742i
$43$	35.1611	+	131.223i	0.124698	+	0.465379i	0.999829	−	0.0185074i	$-0.00589143\pi$
$43$	35.1611	+	131.223i	0.124698	+	0.465379i	−0.875131	+	0.483886i	$0.839225\pi$
$44$	193.950			0.664523
$45$	282.340	+	106.812i	0.935307	+	0.353836i
$46$	6.69773			0.0214680
$47$	−71.4005	−	266.470i	−0.221592	−	0.826993i	−0.983741	−	0.179592i	$-0.942522\pi$
$47$	−71.4005	−	266.470i	−0.221592	−	0.826993i	0.762149	−	0.647401i	$-0.224144\pi$
$48$	−137.181	+	299.850i	−0.412506	+	0.901658i
$49$	−20.5808	+	11.8823i	−0.0600022	+	0.0346423i
$50$	−13.9839	+	12.5433i	−0.0395524	+	0.0354779i
$51$	293.285	−	354.723i	0.805258	−	0.973944i
$52$	−411.724	+	110.321i	−1.09800	+	0.294208i
$53$	−509.361	−	509.361i	−1.32011	−	1.32011i	−0.913680	−	0.406435i	$-0.866772\pi$
$53$	−509.361	−	509.361i	−1.32011	−	1.32011i	−0.406435	−	0.913680i	$-0.633228\pi$
$54$	−10.9372	−	18.0253i	−0.0275622	−	0.0454246i
$55$	129.475	+	239.003i	0.317427	+	0.585948i
$56$	37.1534	+	21.4505i	0.0886577	+	0.0511865i
$57$	20.7179	+	218.520i	0.0481430	+	0.507783i
$58$	−27.3384	−	7.32531i	−0.0618916	−	0.0165838i
$59$	−218.555	−	378.548i	−0.482261	−	0.835301i	0.517532	−	0.855664i	$-0.326851\pi$
$59$	−218.555	−	378.548i	−0.482261	−	0.835301i	−0.999793	+	0.0203635i	$0.993518\pi$
$60$	−462.394	+	31.2135i	−0.994913	+	0.0671607i
$61$	−438.507	+	759.517i	−0.920411	+	1.59420i	−0.121632	+	0.992575i	$0.538813\pi$
$61$	−438.507	+	759.517i	−0.920411	+	1.59420i	−0.798779	+	0.601624i	$0.794520\pi$
$62$	26.2051	−	26.2051i	0.0536782	−	0.0536782i
$63$	434.208	−	210.204i	0.868335	−	0.420369i
$64$		−	503.348i		−	0.983101i
$65$	−410.804	−	433.718i	−0.783907	−	0.827632i
$66$	3.16090	−	18.7202i	0.00589514	−	0.0349136i
$67$	−92.9184	+	346.776i	−0.169430	+	0.632320i	0.828004	+	0.560722i	$0.189476\pi$
$67$	−92.9184	+	346.776i	−0.169430	+	0.632320i	−0.997434	+	0.0715978i	$0.977190\pi$
$68$	−182.888	+	682.547i	−0.326153	+	1.21722i
$69$	−38.5567	+	228.349i	−0.0672707	+	0.398406i
$70$	−0.814223	+	30.0093i	−0.00139026	+	0.0512400i
$71$			534.313i			0.893117i	0.894754	+	0.446559i	$0.147351\pi$
$71$			534.313i			0.893117i	−0.894754	+	0.446559i	$0.852649\pi$
$72$	53.6400	+	36.4099i	0.0877991	+	0.0595964i
$73$	579.639	−	579.639i	0.929337	−	0.929337i	−0.0683265	−	0.997663i	$-0.521766\pi$
$73$	579.639	−	579.639i	0.929337	−	0.929337i	0.997663	+	0.0683265i	$0.0217660\pi$
$74$	−13.5907	+	23.5399i	−0.0213499	+	0.0369791i
$75$	−347.145	−	548.967i	−0.534465	−	0.845190i
$76$	−168.494	−	291.840i	−0.254310	−	0.440478i
$77$	419.591	+	112.429i	0.620998	+	0.166396i
$78$	3.93822	+	41.5379i	0.00571686	+	0.0602980i
$79$	522.214	+	301.501i	0.743718	+	0.429386i	0.823420	−	0.567433i	$-0.192063\pi$
$79$	522.214	+	301.501i	0.743718	+	0.429386i	−0.0797017	+	0.996819i	$0.525397\pi$
$80$	623.830	−	337.948i	0.871828	−	0.472297i
$81$	677.506	−	269.121i	0.929364	−	0.369165i
$82$	−4.02439	−	4.02439i	−0.00541975	−	0.00541975i
$83$	−58.9790	+	15.8034i	−0.0779975	+	0.0208994i	−0.297607	−	0.954689i	$-0.596188\pi$
$83$	−58.9790	+	15.8034i	−0.0779975	+	0.0208994i	0.219609	+	0.975588i	$0.429522\pi$
$84$	−471.934	+	570.795i	−0.613002	+	0.741415i
$85$	−963.189	+	230.278i	−1.22909	+	0.293849i
$86$	−17.6808	+	10.2080i	−0.0221694	+	0.0127995i
$87$	407.124	−	889.893i	0.501704	−	1.09663i
$88$	15.1090	+	56.3875i	0.0183025	+	0.0683060i
$89$	−858.746			−1.02277			−0.511387	−	0.859350i	$-0.670868\pi$
$89$	−858.746			−1.02277			−0.511387	+	0.859350i	$0.670868\pi$
$90$	−4.52311	+	45.1393i	−0.00529753	+	0.0528678i
$91$	−954.676			−1.09975
$92$	−92.0196	−	343.422i	−0.104279	−	0.389176i
$93$	742.569	+	1044.28i	0.827965	+	1.16437i
$94$	35.9039	−	20.7291i	0.0393958	−	0.0227452i
$95$	247.151	−	402.458i	0.266917	−	0.434646i
$96$	−147.281	−	24.8684i	−0.156582	−	0.0264388i
$97$	1300.14	−	348.372i	1.36092	−	0.364658i	0.496767	−	0.867884i	$-0.334520\pi$
$97$	1300.14	−	348.372i	1.36092	−	0.364658i	0.864155	+	0.503226i	$0.167854\pi$
$98$	−2.52535	−	2.52535i	−0.00260305	−	0.00260305i
$99$	620.041	+	215.532i	0.629459	+	0.218806i
$100$	835.274	+	544.682i	0.835274	+	0.544682i
$101$	1564.93	+	903.512i	1.54175	+	0.890127i	0.998729	+	0.0504048i	$0.0160511\pi$
$101$	1564.93	+	903.512i	1.54175	+	0.890127i	0.543016	+	0.839722i	$0.317282\pi$
$102$	62.8994	+	28.7763i	0.0610585	+	0.0279341i
$103$	419.708	+	112.461i	0.401506	+	0.107583i	0.453920	−	0.891042i	$-0.350025\pi$
$103$	419.708	+	112.461i	0.401506	+	0.107583i	−0.0524146	+	0.998625i	$0.516692\pi$
$104$	−64.1480	−	111.108i	−0.0604829	−	0.104760i
$105$	−1018.44	−	200.514i	−0.946564	−	0.186363i
$106$	54.1273	−	93.7512i	0.0495972	−	0.0859049i
$107$	783.841	−	783.841i	0.708194	−	0.708194i	−0.257961	−	0.966155i	$-0.583051\pi$
$107$	783.841	−	783.841i	0.708194	−	0.708194i	0.966155	+	0.257961i	$0.0830506\pi$
$108$	−773.969	+	808.444i	−0.689585	+	0.720302i
$109$		−	348.339i		−	0.306099i	−0.988219	−	0.153050i	$-0.951091\pi$
$109$		−	348.339i		−	0.306099i	0.988219	−	0.153050i	$-0.0489094\pi$
$110$	−29.6578	+	28.0910i	−0.0257069	+	0.0243488i
$111$	−724.319	−	598.868i	−0.619363	−	0.512090i
$112$	293.455	−	1095.19i	0.247579	−	0.923979i
$113$	125.346	−	467.797i	0.104350	−	0.389439i	−0.893921	−	0.448225i	$-0.852056\pi$
$113$	125.346	−	467.797i	0.104350	−	0.389439i	0.998271	+	0.0587860i	$0.0187230\pi$
$114$	−30.9147	+	11.5069i	−0.0253985	+	0.00945370i
$115$	361.767	−	342.654i	0.293347	−	0.277849i
$116$			1502.40i			1.20254i
$117$	−1438.85	−	104.853i	−1.13693	−	0.0828517i
$118$	46.4495	−	46.4495i	0.0362375	−	0.0362375i
$119$	−791.320	+	1370.61i	−0.609581	+	1.05583i
$120$	−45.0960	−	132.001i	−0.0343057	−	0.100417i
$121$	−369.955	−	640.781i	−0.277953	−	0.481428i
$122$	−127.308	−	34.1121i	−0.0944749	−	0.0253145i
$123$	160.373	−	114.038i	0.117563	−	0.0835975i
$124$	−1703.68	−	983.618i	−1.23383	−	0.712351i
$125$	−113.602	+	1392.92i	−0.0812872	+	0.996691i
$126$	47.4023	+	54.8540i	0.0335153	+	0.0387840i
$127$	535.743	+	535.743i	0.374327	+	0.374327i	0.869050	−	0.494723i	$-0.164731\pi$
$127$	535.743	+	535.743i	0.374327	+	0.374327i	−0.494723	+	0.869050i	$0.664731\pi$
$128$	295.195	−	79.0972i	0.203842	−	0.0546193i
$129$	−246.245	−	661.565i	−0.168067	−	0.451532i
$130$	46.9803	−	76.5024i	0.0316957	−	0.0516131i
$131$	−1165.71	+	673.021i	−0.777467	+	0.448871i	−0.835532	−	0.549442i	$-0.814840\pi$
$131$	−1165.71	+	673.021i	−0.777467	+	0.448871i	0.0580646	+	0.998313i	$0.481507\pi$
$132$	−1003.29	+	95.1223i	−0.661556	+	0.0627222i
$133$	−195.346	−	729.040i	−0.127358	−	0.475307i
$134$	−53.9525			−0.0347820
$135$	−1512.92	−	414.061i	−0.964529	−	0.263976i
$136$	−212.686			−0.134101
$137$	198.287	+	740.019i	0.123656	+	0.461489i	0.999788	−	0.0205810i	$-0.00655160\pi$
$137$	198.287	+	740.019i	0.123656	+	0.461489i	−0.876132	+	0.482070i	$0.839885\pi$
$138$	−34.6471	+	3.28489i	−0.0213721	+	0.00202629i
$139$	856.403	−	494.444i	0.522584	−	0.301714i	−0.215407	−	0.976524i	$-0.569108\pi$
$139$	856.403	−	494.444i	0.522584	−	0.301714i	0.737991	+	0.674810i	$0.235775\pi$
$140$	1549.90	−	370.547i	0.935644	−	0.223693i
$141$	500.041	+	1343.42i	0.298660	+	0.802386i
$142$	−77.5614	+	20.7825i	−0.0458367	+	0.0122819i
$143$	−918.570	−	918.570i	−0.537166	−	0.537166i
$144$	562.568	−	1618.39i	0.325560	−	0.936568i
$145$	−1851.40	+	1002.96i	−1.06035	+	0.574424i
$146$	106.686	+	61.5954i	0.0604755	+	0.0349155i
$147$	100.636	−	71.5605i	0.0564646	−	0.0401511i
$148$	1393.71	+	373.444i	0.774071	+	0.207412i
$149$	62.8174	+	108.803i	0.0345383	+	0.0598221i	0.882778	−	0.469791i	$-0.155671\pi$
$149$	62.8174	+	108.803i	0.0345383	+	0.0598221i	−0.848240	+	0.529613i	$0.822337\pi$
$150$	66.1861	−	71.7444i	0.0360271	−	0.0390527i
$151$	569.572	−	986.527i	0.306961	−	0.531672i	−0.670735	−	0.741697i	$-0.734021\pi$
$151$	569.572	−	986.527i	0.306961	−	0.531672i	0.977696	+	0.210025i	$0.0673546\pi$
$152$	71.7215	−	71.7215i	0.0382723	−	0.0382723i
$153$	−1343.18	+	1978.81i	−0.709735	+	1.04560i
$154$			65.2812i			0.0341592i
$155$	74.7784	−	2756.07i	0.0387506	−	1.42821i
$156$	2075.72	−	772.616i	1.06533	−	0.396531i
$157$	−449.715	+	1678.36i	−0.228606	+	0.853170i	0.752321	+	0.658796i	$0.228934\pi$
$157$	−449.715	+	1678.36i	−0.228606	+	0.853170i	−0.980928	+	0.194374i	$0.937732\pi$
$158$	−23.4542	+	87.5322i	−0.0118096	+	0.0440740i
$159$	2884.71	+	2385.08i	1.43882	+	1.18962i
$160$	221.006	+	233.333i	0.109200	+	0.115291i
$161$		−	796.301i		−	0.389797i
$162$	65.4180	+	87.8797i	0.0317267	+	0.0426203i
$163$	−140.351	+	140.351i	−0.0674424	+	0.0674424i	−0.740023	−	0.672581i	$-0.765186\pi$
$163$	−140.351	+	140.351i	−0.0674424	+	0.0674424i	0.672581	+	0.740023i	$0.265186\pi$
$164$	−151.057	+	261.639i	−0.0719243	+	0.124576i
$165$	−786.989	−	1172.85i	−0.371315	−	0.553371i
$166$	−4.58807	−	7.94677i	−0.00214520	−	0.00371559i
$167$	−1170.94	−	313.753i	−0.542577	−	0.145383i	−0.0228869	−	0.999738i	$-0.507286\pi$
$167$	−1170.94	−	313.753i	−0.542577	−	0.145383i	−0.519690	+	0.854355i	$0.673952\pi$
$168$	−202.713	−	92.7408i	−0.0930932	−	0.0425899i
$169$	569.816	+	328.983i	0.259361	+	0.149742i
$170$	−70.8913	−	130.861i	−0.0319830	−	0.0590385i
$171$	−214.345	−	1120.23i	−0.0958561	−	0.500972i
$172$	766.325	+	766.325i	0.339719	+	0.339719i
$173$	563.020	−	150.861i	0.247431	−	0.0662990i	−0.132972	−	0.991120i	$-0.542452\pi$
$173$	563.020	−	150.861i	0.247431	−	0.0662990i	0.380403	+	0.924821i	$0.375785\pi$
$174$	145.013	+	24.4854i	0.0631805	+	0.0106680i
$175$	1491.29	+	1662.56i	0.644177	+	0.718158i
$176$	1336.13	−	771.412i	0.572240	−	0.330383i
$177$	1316.23	+	1851.02i	0.558949	+	0.786052i
$178$	−33.4016	−	124.656i	−0.0140649	−	0.0524909i
$179$	1581.27			0.660276			0.330138	−	0.943933i	$-0.392905\pi$
$179$	1581.27			0.660276			0.330138	+	0.943933i	$0.392905\pi$
$180$	2376.63	−	388.246i	0.984132	−	0.160768i
$181$	−1833.95			−0.753128			−0.376564	−	0.926391i	$-0.622895\pi$
$181$	−1833.95			−0.753128			−0.376564	+	0.926391i	$0.622895\pi$
$182$	−37.1328	−	138.582i	−0.0151235	−	0.0564415i
$183$	1895.87	−	4144.01i	0.765831	−	1.67396i
$184$	92.6755	−	53.5062i	0.0371311	−	0.0214377i
$185$	470.212	+	1966.77i	0.186868	+	0.781619i
$186$	−122.705	+	148.410i	−0.0483720	+	0.0585050i
$187$	−2080.16	+	557.378i	−0.813458	+	0.217965i
$188$	−1556.15	−	1556.15i	−0.603692	−	0.603692i
$189$	−2143.04	+	1300.33i	−0.824781	+	0.500452i
$190$	68.0343	+	20.2227i	0.0259775	+	0.00772162i
$191$	−3785.91	−	2185.80i	−1.43424	−	0.828057i	−0.436796	−	0.899561i	$-0.643887\pi$
$191$	−3785.91	−	2185.80i	−1.43424	−	0.828057i	−0.997440	+	0.0715042i	$0.977220\pi$
$192$	246.866	+	2603.80i	0.0927918	+	0.978712i
$193$	−540.817	−	144.912i	−0.201704	−	0.0540464i	0.156552	−	0.987670i	$-0.449962\pi$
$193$	−540.817	−	144.912i	−0.201704	−	0.0540464i	−0.358256	+	0.933623i	$0.616629\pi$
$194$	101.140	+	175.180i	0.0374300	+	0.0648307i
$195$	2337.79	+	2042.12i	0.858525	+	0.749946i
$196$	−94.7901	+	164.181i	−0.0345445	+	0.0598329i
$197$	1223.65	−	1223.65i	0.442544	−	0.442544i	−0.450322	−	0.892866i	$-0.648691\pi$
$197$	1223.65	−	1223.65i	0.442544	−	0.442544i	0.892866	+	0.450322i	$0.148691\pi$
$198$	−7.16989	+	98.3890i	−0.00257344	+	0.0353141i
$199$		−	1137.16i		−	0.405082i	−0.979274	−	0.202541i	$-0.935080\pi$
$199$		−	1137.16i		−	0.405082i	0.979274	−	0.202541i	$-0.0649199\pi$
$200$	−93.2878	+	285.273i	−0.0329822	+	0.100859i
$201$	310.587	−	1839.43i	0.108991	−	0.645489i
$202$	−70.2856	+	262.309i	−0.0244816	+	0.0913664i
$203$	−870.915	+	3250.30i	−0.301114	+	1.12377i
$204$	611.317	−	3620.48i	0.209808	−	1.24257i
$205$	−423.257	−	11.4839i	−0.144203	−	0.00391255i
$206$			65.2995i			0.0220856i
$207$	87.4584	−	1200.15i	0.0293661	−	0.402977i
$208$	−2397.59	+	2397.59i	−0.799246	+	0.799246i
$209$	513.510	−	889.426i	0.169953	−	0.294368i
$210$	−10.5061	−	155.636i	−0.00345233	−	0.0511425i
$211$	2550.70	+	4417.95i	0.832217	+	1.44144i	0.896276	+	0.443496i	$0.146262\pi$
$211$	2550.70	+	4417.95i	0.832217	+	1.44144i	−0.0640596	+	0.997946i	$0.520405\pi$
$212$	−5550.68	−	1487.30i	−1.79822	−	0.481831i
$213$	−262.053	−	2763.98i	−0.0842985	−	0.889130i
$214$	144.271	+	83.2950i	0.0460849	+	0.0266071i
$215$	−432.760	+	1455.91i	−0.137274	+	0.461826i
$216$	−295.335	−	162.039i	−0.0930323	−	0.0510433i
$217$	−3115.55	−	3115.55i	−0.974642	−	0.974642i
$218$	50.5652	−	13.5489i	0.0157097	−	0.00420939i
$219$	−2714.16	+	3282.73i	−0.837470	+	1.01290i
$220$	1847.81	+	1134.75i	0.566271	+	0.347748i
$221$	4098.81	−	2366.45i	1.24758	−	0.720292i
$222$	58.7592	−	128.436i	0.0177642	−	0.0388292i
$223$	−867.535	−	3237.69i	−0.260513	−	0.972249i	−0.964940	−	0.262472i	$-0.915462\pi$
$223$	−867.535	−	3237.69i	−0.260513	−	0.972249i	0.704427	−	0.709777i	$-0.251204\pi$
$224$	513.601			0.153198
$225$	2065.01	+	2669.53i	0.611854	+	0.790971i
$226$	72.7812			0.0214218
$227$	1173.62	+	4379.99i	0.343152	+	1.28066i	0.894756	+	0.446556i	$0.147350\pi$
$227$	1173.62	+	4379.99i	0.343152	+	1.28066i	−0.551603	+	0.834107i	$0.685984\pi$
$228$	1014.74	+	1427.04i	0.294750	+	0.414508i
$229$	−161.303	+	93.1281i	−0.0465466	+	0.0268737i	−0.523093	−	0.852276i	$-0.675222\pi$
$229$	−161.303	+	93.1281i	−0.0465466	+	0.0268737i	0.476546	+	0.879149i	$0.341889\pi$
$230$	63.8112	+	39.1866i	0.0182938	+	0.0112343i
$231$	−2225.67	−	375.803i	−0.633931	−	0.107039i
$232$	−436.797	+	117.039i	−0.123608	+	0.0331208i
$233$	374.906	+	374.906i	0.105412	+	0.105412i	0.757846	−	0.652434i	$-0.226252\pi$
$233$	374.906	+	374.906i	0.105412	+	0.105412i	−0.652434	+	0.757846i	$0.726252\pi$
$234$	−40.7444	−	212.942i	−0.0113827	−	0.0594892i
$235$	878.791	−	2956.48i	0.243941	−	0.820679i
$236$	−3019.83	−	1743.50i	−0.832942	−	0.480900i
$237$	−2849.26	−	1303.53i	−0.780926	−	0.357272i
$238$	−229.737	−	61.5580i	−0.0625700	−	0.0167656i
$239$	−2877.36	−	4983.73i	−0.778748	−	1.34883i	−0.932663	−	0.360748i	$-0.882522\pi$
$239$	−2877.36	−	4983.73i	−0.778748	−	1.34883i	0.153915	−	0.988084i	$-0.450812\pi$
$240$	−3061.30	+	2054.15i	−0.823357	+	0.552478i
$241$	1150.77	−	1993.20i	0.307584	−	0.532751i	−0.670249	−	0.742136i	$-0.733813\pi$
$241$	1150.77	−	1993.20i	0.307584	−	0.532751i	0.977833	+	0.209385i	$0.0671462\pi$
$242$	78.6266	−	78.6266i	0.0208856	−	0.0208856i
$243$	−3372.72	+	1724.43i	−0.890371	+	0.455236i
$244$			6996.31i			1.83563i
$245$	−265.599	−	7.20631i	−0.0692591	−	0.00187916i
$246$	22.7917	+	18.8442i	0.00590710	+	0.00488400i
$247$	−584.183	+	2180.20i	−0.150489	+	0.561631i
$248$	153.251	−	571.940i	0.0392397	−	0.146444i
$249$	297.345	−	110.676i	0.0756766	−	0.0281680i
$250$	−206.616	+	37.6880i	−0.0522701	+	0.00953438i
$251$			1875.89i			0.471734i	0.971785	+	0.235867i	$0.0757929\pi$
$251$			1875.89i			0.471734i	−0.971785	+	0.235867i	$0.924207\pi$
$252$	2161.35	−	3184.16i	0.540286	−	0.795964i
$253$	766.186	−	766.186i	0.190394	−	0.190394i
$254$	−56.9308	+	98.6071i	−0.0140636	+	0.0243589i
$255$	4869.59	−	1663.61i	1.19587	−	0.408547i
$256$	−1990.43	−	3447.52i	−0.485944	−	0.841680i
$257$	4371.51	+	1171.34i	1.06104	+	0.284305i	0.746807	−	0.665041i	$-0.231586\pi$
$257$	4371.51	+	1171.34i	1.06104	+	0.284305i	0.314233	+	0.949346i	$0.398253\pi$
$258$	86.4555	−	61.4772i	0.0208623	−	0.0148349i
$259$	2798.68	+	1615.82i	0.671435	+	0.387653i
$260$	−4568.07	−	1357.82i	−1.08961	−	0.323880i
$261$	−1669.59	+	4803.05i	−0.395957	+	1.13909i
$262$	−143.037	−	143.037i	−0.0337285	−	0.0337285i
$263$	5538.89	−	1484.14i	1.29864	−	0.347970i	0.457705	−	0.889104i	$-0.348672\pi$
$263$	5538.89	−	1484.14i	1.29864	−	0.347970i	0.840936	+	0.541134i	$0.182005\pi$
$264$	−105.813	−	284.280i	−0.0246680	−	0.0662736i
$265$	−1872.69	−	7832.95i	−0.434108	−	1.81575i
$266$	98.2300	−	56.7131i	0.0226424	−	0.0130726i
$267$	4442.25	−	421.171i	1.01821	−	0.0965364i
$268$	741.249	+	2766.38i	0.168951	+	0.630535i
$269$	6912.48			1.56677			0.783386	−	0.621536i	$-0.213491\pi$
$269$	6912.48			1.56677			0.783386	+	0.621536i	$0.213491\pi$
$270$	1.25933	−	235.722i	0.000283853	−	0.0531318i
$271$	5767.28			1.29276			0.646379	−	0.763017i	$-0.276283\pi$
$271$	5767.28			1.29276			0.646379	+	0.763017i	$0.276283\pi$
$272$	1454.83	+	5429.50i	0.324309	+	1.21034i
$273$	4938.50	−	468.219i	1.09484	−	0.103802i
$274$	−99.7092	+	57.5671i	−0.0219841	+	0.0126925i
$275$	−164.791	+	3034.57i	−0.0361356	+	0.665424i
$276$	644.444	+	1731.38i	0.140547	+	0.377596i
$277$	3193.75	−	855.762i	0.692757	−	0.185624i	0.104773	−	0.994496i	$-0.466588\pi$
$277$	3193.75	−	855.762i	0.692757	−	0.185624i	0.587984	+	0.808872i	$0.299922\pi$
$278$	105.084	+	105.084i	0.0226710	+	0.0226710i
$279$	−4353.44	−	5037.80i	−0.934170	−	1.08102i
$280$	228.470	+	421.739i	0.0487631	+	0.0900134i
$281$	1619.72	+	935.145i	0.343859	+	0.198527i	0.661977	−	0.749524i	$-0.269718\pi$
$281$	1619.72	+	935.145i	0.343859	+	0.198527i	−0.318118	+	0.948051i	$0.603051\pi$
$282$	−175.563	+	124.840i	−0.0370730	+	0.0263621i
$283$	−2388.93	−	640.112i	−0.501792	−	0.134455i	−0.000960478	−	1.00000i	$-0.500306\pi$
$283$	−2388.93	−	640.112i	−0.501792	−	0.134455i	−0.500832	+	0.865545i	$0.666972\pi$
$284$	2131.22	+	3691.38i	0.445298	+	0.771278i
$285$	−1081.11	+	2203.11i	−0.224701	+	0.457899i
$286$	97.6120	−	169.069i	0.0201815	−	0.0349555i
$287$	−478.464	+	478.464i	−0.0984071	+	0.0984071i
$288$	774.077	+	56.4092i	0.158378	+	0.0115415i
$289$		−	2933.09i		−	0.597006i
$290$	−217.602	−	229.740i	−0.0440622	−	0.0465200i
$291$	−6554.71	+	2439.76i	−1.32043	+	0.491483i
$292$	1692.51	−	6316.53i	0.339200	−	1.26591i
$293$	−1084.97	+	4049.15i	−0.216329	+	0.807350i	0.769366	+	0.638809i	$0.220572\pi$
$293$	−1084.97	+	4049.15i	−0.216329	+	0.807350i	−0.985695	+	0.168542i	$0.946094\pi$
$294$	14.3021	+	11.8250i	0.00283712	+	0.00234574i
$295$	132.548	−	4885.23i	0.0261601	−	0.964167i
$296$			434.290i			0.0852790i
$297$	−3313.15	−	810.840i	−0.647301	−	0.158417i
$298$	−13.3506	+	13.3506i	−0.00259524	+	0.00259524i
$299$	−1190.67	+	2062.31i	−0.230296	+	0.398884i
$300$	−4587.97	−	2407.96i	−0.882956	−	0.463412i
$301$	1213.64	+	2102.09i	0.232403	+	0.402534i
$302$	165.359	+	44.3078i	0.0315078	+	0.00844248i
$303$	−8538.43	−	3906.31i	−1.61888	−	0.740633i
$304$	−2321.52	−	1340.33i	−0.437988	−	0.252872i
$305$	−8621.50	+	4670.54i	−1.61858	+	0.876834i
$306$	−339.489	−	118.010i	−0.0634226	−	0.0220463i
$307$	1824.30	+	1824.30i	0.339147	+	0.339147i	0.856046	−	0.516899i	$-0.172914\pi$
$307$	1824.30	+	1824.30i	0.339147	+	0.339147i	−0.516899	+	0.856046i	$0.672914\pi$
$308$	3347.25	−	896.894i	0.619245	−	0.165926i
$309$	−2226.29	−	375.908i	−0.409868	−	0.0692060i
$310$	402.981	−	96.3443i	0.0738316	−	0.0176516i
$311$	2249.25	−	1298.60i	0.410107	−	0.236775i	−0.280729	−	0.959787i	$-0.590576\pi$
$311$	2249.25	−	1298.60i	0.410107	−	0.236775i	0.690836	+	0.723012i	$0.257243\pi$
$312$	386.327	+	543.293i	0.0701008	+	0.0985830i
$313$	1233.84	+	4604.75i	0.222814	+	0.831553i	0.983269	+	0.182162i	$0.0583094\pi$
$313$	1233.84	+	4604.75i	0.222814	+	0.831553i	−0.760455	+	0.649391i	$0.775024\pi$
$314$	−261.124			−0.0469302
$315$	5366.67	+	537.758i	0.959929	+	0.0961880i
$316$	4810.39			0.856347
$317$	−1320.36	−	4927.65i	−0.233939	−	0.873074i	−0.978624	−	0.205657i	$-0.934067\pi$
$317$	−1320.36	−	4927.65i	−0.233939	−	0.873074i	0.744685	−	0.667417i	$-0.232600\pi$
$318$	−234.018	+	511.517i	−0.0412675	+	0.0902027i
$319$	−3965.35	+	2289.40i	−0.695978	+	0.401823i
$320$	2944.95	−	4795.54i	0.514462	−	0.837746i
$321$	−3670.34	+	4439.21i	−0.638189	+	0.771877i
$322$	115.592	−	30.9727i	0.0200052	−	0.00536038i
$323$	2645.84	+	2645.84i	0.455785	+	0.455785i
$324$	3607.20	−	4561.64i	0.618519	−	0.782174i
$325$	−1376.28	−	6535.65i	−0.234899	−	1.11548i
$326$	−25.8325	−	14.9144i	−0.00438874	−	0.00253384i
$327$	170.842	+	1801.94i	0.0288917	+	0.304733i
$328$	−87.8345	−	23.5352i	−0.0147861	−	0.00396193i
$329$	−2464.51	−	4268.65i	−0.412987	−	0.715315i
$330$	139.641	−	159.859i	0.0232940	−	0.0266665i
$331$	−2201.28	+	3812.72i	−0.365538	+	0.633130i	−0.988862	−	0.148833i	$-0.952448\pi$
$331$	−2201.28	+	3812.72i	−0.365538	+	0.633130i	0.623324	+	0.781963i	$0.285782\pi$
$332$	−344.430	+	344.430i	−0.0569369	+	0.0569369i
$333$	4040.58	+	2742.67i	0.664933	+	0.451344i
$334$		−	182.179i		−	0.0298454i
$335$	−2914.15	+	2760.19i	−0.475275	+	0.450166i
$336$	−980.895	+	5809.29i	−0.159263	+	0.943222i
$337$	1406.53	−	5249.26i	0.227355	−	0.848502i	−0.754092	−	0.656769i	$-0.771923\pi$
$337$	1406.53	−	5249.26i	0.227355	−	0.848502i	0.981447	−	0.191733i	$-0.0614107\pi$
$338$	−25.5921	+	95.5111i	−0.00411842	+	0.0153702i
$339$	−418.978	+	2481.37i	−0.0671261	+	0.397550i
$340$	−5735.82	+	5432.79i	−0.914907	+	0.866572i
$341$		−	5995.44i		−	0.952116i
$342$	154.277	−	74.6868i	0.0243928	−	0.0118088i
$343$	−4633.70	+	4633.70i	−0.729435	+	0.729435i
$344$	−163.098	+	282.494i	−0.0255629	+	0.0442763i
$345$	−1703.35	+	1949.96i	−0.265812	+	0.304297i
$346$	43.7982	+	75.8607i	0.00680522	+	0.0117870i
$347$	−7049.21	−	1888.83i	−1.09055	−	0.292213i	−0.331640	−	0.943406i	$-0.607602\pi$
$347$	−7049.21	−	1888.83i	−1.09055	−	0.292213i	−0.758912	+	0.651193i	$0.774269\pi$
$348$	−736.851	−	7771.86i	−0.113504	−	1.19717i
$349$	1143.62	+	660.269i	0.175406	+	0.101270i	0.585132	−	0.810938i	$-0.301043\pi$
$349$	1143.62	+	660.269i	0.175406	+	0.101270i	−0.409727	+	0.912208i	$0.634376\pi$
$350$	−183.334	+	281.144i	−0.0279989	+	0.0429364i
$351$	7494.51	−	163.281i	1.13968	−	0.0248299i
$352$	494.177	+	494.177i	0.0748287	+	0.0748287i
$353$	6474.52	−	1734.84i	0.976214	−	0.261576i	0.264765	−	0.964313i	$-0.414706\pi$
$353$	6474.52	−	1734.84i	0.976214	−	0.261576i	0.711450	+	0.702737i	$0.248039\pi$
$354$	−217.500	+	263.062i	−0.0326554	+	0.0394960i
$355$	−3126.12	+	5090.55i	−0.467372	+	0.761066i
$356$	−5932.77	+	3425.29i	−0.883248	+	0.509943i
$357$	3421.25	−	7478.19i	0.507204	−	1.10865i
$358$	61.5045	+	229.538i	0.00907993	+	0.0338868i
$359$	−2067.92			−0.304013			−0.152007	−	0.988379i	$-0.548573\pi$
$359$	−2067.92			−0.304013			−0.152007	+	0.988379i	$0.548573\pi$
$360$	298.019	+	660.720i	0.0436306	+	0.0967305i
$361$	5074.55			0.739838
$362$	−71.3327	−	266.217i	−0.0103568	−	0.0386521i
$363$	2228.03	+	3133.28i	0.322152	+	0.453044i
$364$	−6595.52	+	3807.92i	−0.949723	+	0.548323i
$365$	8913.68	−	2131.07i	1.27826	−	0.305604i
$366$	675.290	+	114.022i	0.0964425	+	0.0162843i
$367$	−3152.64	+	844.747i	−0.448410	+	0.120151i	−0.475955	−	0.879469i	$-0.657898\pi$
$367$	−3152.64	+	844.747i	−0.448410	+	0.120151i	0.0275453	+	0.999621i	$0.491231\pi$
$368$	−1999.85	−	1999.85i	−0.283286	−	0.283286i
$369$	−773.670	+	668.570i	−0.109148	+	0.0943208i
$370$	−267.208	+	144.755i	−0.0375446	+	0.0203391i
$371$	−11146.2	−	6435.26i	−1.55979	−	0.900544i
$372$	9295.46	+	4252.65i	1.29556	+	0.592714i
$373$	−6585.44	−	1764.56i	−0.914159	−	0.244948i	−0.229072	−	0.973409i	$-0.573569\pi$
$373$	−6585.44	−	1764.56i	−0.914159	−	0.244948i	−0.685087	+	0.728461i	$0.740236\pi$
$374$	−161.819	−	280.279i	−0.0223729	−	0.0387510i
$375$	−95.4946	−	7261.22i	−0.0131502	−	0.999914i
$376$	331.198	−	573.651i	0.0454261	−	0.0786803i
$377$	7115.56	−	7115.56i	0.972070	−	0.972070i
$378$	−272.113	−	260.509i	−0.0370264	−	0.0354474i
$379$		−	789.777i		−	0.107040i	−0.998567	−	0.0535200i	$-0.982956\pi$
$379$		−	789.777i		−	0.107040i	0.998567	−	0.0535200i	$-0.0170441\pi$
$380$	102.187	−	3766.25i	0.0137950	−	0.508433i
$381$	−3034.13	−	2508.62i	−0.407987	−	0.337324i
$382$	170.036	−	634.585i	0.0227744	−	0.0849952i
$383$	−3290.56	+	12280.5i	−0.439008	+	1.63840i	0.292282	+	0.956332i	$0.405585\pi$
$383$	−3290.56	+	12280.5i	−0.439008	+	1.63840i	−0.731290	+	0.682067i	$0.761081\pi$
$384$	−1488.24	+	553.944i	−0.197777	+	0.0736155i
$385$	3339.77	+	3526.05i	0.442105	+	0.466765i
$386$		−	84.1420i		−	0.0110951i
$387$	1598.28	+	3301.48i	0.209935	+	0.433652i
$388$	7592.66	−	7592.66i	0.993451	−	0.993451i
$389$	−2988.37	+	5176.01i	−0.389503	+	0.674638i	−0.992383	−	0.123193i	$-0.960686\pi$
$389$	−2988.37	+	5176.01i	−0.389503	+	0.674638i	0.602880	+	0.797832i	$0.294020\pi$
$390$	−205.507	+	418.785i	−0.0266826	+	0.0543744i
$391$	1973.87	+	3418.84i	0.255302	+	0.442195i
$392$	−55.1172	−	14.7686i	−0.00710163	−	0.00190288i
$393$	5700.06	−	4053.23i	0.731629	−	0.520250i
$394$	225.220	+	130.031i	0.0287980	+	0.0166266i
$395$	3211.28	+	5927.81i	0.409056	+	0.755090i
$396$	5143.34	−	984.127i	0.652683	−	0.124884i
$397$	−4136.29	−	4136.29i	−0.522908	−	0.522908i	0.395541	−	0.918448i	$-0.370557\pi$
$397$	−4136.29	−	4136.29i	−0.522908	−	0.522908i	−0.918448	+	0.395541i	$0.870557\pi$
$398$	165.072	−	44.2308i	0.0207897	−	0.00557058i
$399$	1368.07	+	3675.48i	0.171652	+	0.461164i
$400$	7920.64	+	430.127i	0.990080	+	0.0537659i
$401$	2724.61	−	1573.05i	0.339303	−	0.195896i	−0.320661	−	0.947194i	$-0.603905\pi$
$401$	2724.61	−	1573.05i	0.339303	−	0.195896i	0.659964	+	0.751298i	$0.270572\pi$
$402$	279.094	−	26.4609i	0.0346267	−	0.00328296i
$403$	3410.29	+	12727.4i	0.421535	+	1.57319i
$404$	14415.4			1.77523
$405$	8029.34	+	1399.91i	0.985139	+	0.171758i
$406$	−505.691			−0.0618153
$407$	1138.13	+	4247.55i	0.138611	+	0.517305i
$408$	1100.22	−	104.312i	0.133502	−	0.0126573i
$409$	5590.40	−	3227.62i	0.675862	−	0.390209i	−0.122432	−	0.992477i	$-0.539069\pi$
$409$	5590.40	−	3227.62i	0.675862	−	0.390209i	0.798294	+	0.602268i	$0.205736\pi$
$410$	−14.7959	−	61.8870i	−0.00178223	−	0.00745459i
$411$	−1388.67	−	3730.83i	−0.166662	−	0.447758i
$412$	3348.19	−	897.144i	0.400372	−	0.107279i
$413$	−5522.44	−	5522.44i	−0.657969	−	0.657969i
$414$	177.617	−	33.9852i	0.0210855	−	0.00403450i
$415$	−654.371	−	194.507i	−0.0774019	−	0.0230071i
$416$	−1330.15	−	767.964i	−0.156770	−	0.0905109i
$417$	−4187.63	+	2977.76i	−0.491773	+	0.349692i
$418$	149.083	+	39.9467i	0.0174447	+	0.00467430i
$419$	−2382.20	−	4126.08i	−0.277752	−	0.481080i	0.693074	−	0.720866i	$-0.256256\pi$
$419$	−2382.20	−	4126.08i	−0.277752	−	0.481080i	−0.970826	+	0.239787i	$0.922923\pi$
$420$	−7835.81	+	2676.97i	−0.910353	+	0.311006i
$421$	−2072.95	+	3590.45i	−0.239974	+	0.415648i	−0.960707	−	0.277566i	$-0.910472\pi$
$421$	−2072.95	+	3590.45i	−0.239974	+	0.415648i	0.720732	+	0.693214i	$0.243806\pi$
$422$	−542.102	+	542.102i	−0.0625334	+	0.0625334i
$423$	−3245.57	−	6704.21i	−0.373061	−	0.770614i
$424$		−	1729.63i		−	0.198109i
$425$	−10523.9	−	3441.43i	−1.20114	−	0.392786i
$426$	391.029	−	145.547i	0.0444728	−	0.0165534i
$427$	−4055.63	+	15135.8i	−0.459639	+	1.71540i
$428$	2288.77	−	8541.80i	0.258485	−	0.964680i
$429$	5202.23	+	4301.21i	0.585469	+	0.484066i
$430$	−228.174	−	6.19090i	−0.0255896	−	0.000694306i
$431$		−	9106.66i		−	1.01775i	−0.860839	−	0.508877i	$-0.830061\pi$
$431$		−	9106.66i		−	1.01775i	0.860839	−	0.508877i	$-0.169939\pi$
$432$	−2116.40	+	8647.77i	−0.235707	+	0.963115i
$433$	−1195.77	+	1195.77i	−0.132714	+	0.132714i	−0.770343	−	0.637629i	$-0.779915\pi$
$433$	−1195.77	+	1195.77i	−0.132714	+	0.132714i	0.637629	+	0.770343i	$0.279915\pi$
$434$	331.074	−	573.438i	0.0366177	−	0.0634237i
$435$	9085.30	−	6096.29i	1.00140	−	0.671942i
$436$	−1389.42	−	2406.55i	−0.152617	−	0.264341i
$437$	−1818.52	−	487.271i	−0.199065	−	0.0533394i
$438$	−582.093	−	266.306i	−0.0635011	−	0.0290516i
$439$	1755.76	+	1013.69i	0.190883	+	0.110207i	0.592396	−	0.805647i	$-0.298182\pi$
$439$	1755.76	+	1013.69i	0.190883	+	0.110207i	−0.401513	+	0.915853i	$0.631515\pi$
$440$	−185.960	+	625.618i	−0.0201484	+	0.0677845i
$441$	−485.487	+	419.536i	−0.0524228	+	0.0453013i
$442$	502.942	+	502.942i	0.0541234	+	0.0541234i
$443$	−954.096	+	255.649i	−0.102326	+	0.0274182i	−0.309619	−	0.950861i	$-0.600201\pi$
$443$	−954.096	+	255.649i	−0.102326	+	0.0274182i	0.207293	+	0.978279i	$0.433535\pi$
$444$	−7392.77	−	1248.27i	−0.790192	−	0.133424i
$445$	−8181.51	−	5024.29i	−0.871553	−	0.535223i
$446$	436.242	−	251.864i	0.0463154	−	0.0267402i
$447$	−378.314	−	532.024i	−0.0400305	−	0.0562951i
$448$	−2327.66	−	8686.95i	−0.245473	−	0.916116i
$449$	−10097.9			−1.06136			−0.530681	−	0.847572i	$-0.678064\pi$
$449$	−10097.9			−1.06136			−0.530681	+	0.847572i	$0.678064\pi$
$450$	−307.191	+	403.592i	−0.0321802	+	0.0422789i
$451$	−920.738			−0.0961327
$452$	−999.935	−	3731.81i	−0.104055	−	0.388340i
$453$	−2462.53	+	5382.60i	−0.255408	+	0.558271i
$454$	−590.155	+	340.726i	−0.0610074	+	0.0352226i
$455$	−9095.46	−	5585.55i	−0.937147	−	0.575504i
$456$	−335.836	+	406.188i	−0.0344890	+	0.0417138i
$457$	−10496.3	+	2812.48i	−1.07439	+	0.287883i	−0.752297	−	0.658825i	$-0.771054\pi$
$457$	−10496.3	+	2812.48i	−1.07439	+	0.287883i	−0.322096	+	0.946707i	$0.604387\pi$
$458$	−19.7925	−	19.7925i	−0.00201931	−	0.00201931i
$459$	5977.69	−	10895.0i	0.607876	−	1.10792i
$460$	1132.57	−	3810.26i	0.114796	−	0.386205i
$461$	16323.3	+	9424.28i	1.64914	+	0.952131i	0.977415	+	0.211330i	$0.0677796\pi$
$461$	16323.3	+	9424.28i	1.64914	+	0.952131i	0.671725	+	0.740801i	$0.265554\pi$
$462$	−32.0171	−	337.697i	−0.00322418	−	0.0340067i
$463$	−941.888	−	252.378i	−0.0945426	−	0.0253326i	0.211238	−	0.977435i	$-0.432251\pi$
$463$	−941.888	−	252.378i	−0.0945426	−	0.0253326i	−0.305780	+	0.952102i	$0.598917\pi$
$464$	5975.63	+	10350.1i	0.597870	+	1.03554i
$465$	964.883	+	14293.7i	0.0962266	+	1.42549i
$466$	−39.8394	+	69.0039i	−0.00396035	+	0.00685953i
$467$	−12141.4	+	12141.4i	−1.20308	+	1.20308i	−0.229854	+	0.973225i	$0.573825\pi$
$467$	−12141.4	+	12141.4i	−1.20308	+	1.20308i	−0.973225	+	0.229854i	$0.926175\pi$
$468$	−10358.7	+	5014.74i	−1.02314	+	0.495313i
$469$			6414.47i			0.631541i
$470$	463.346	+	12.5717i	0.0454736	+	0.00123380i
$471$	1503.21	−	8902.65i	0.147058	−	0.870939i
$472$	271.643	−	1013.79i	0.0264902	−	0.0988629i
$473$	−854.848	+	3190.34i	−0.0830993	+	0.310131i
$474$	78.3974	−	464.303i	0.00759686	−	0.0449919i
$475$	4709.35	−	2388.32i	0.454904	−	0.230703i
$476$			12625.4i			1.21572i
$477$	−16092.3	−	10923.1i	−1.54468	−	1.04850i
$478$	611.526	−	611.526i	0.0585158	−	0.0585158i
$479$	8272.10	−	14327.7i	0.789064	−	1.36670i	−0.137476	−	0.990505i	$-0.543899\pi$
$479$	8272.10	−	14327.7i	0.789064	−	1.36670i	0.926541	−	0.376195i	$-0.122768\pi$
$480$	−1257.69	−	1098.63i	−0.119595	−	0.104470i
$481$	−4832.12	−	8369.48i	−0.458058	−	0.793380i
$482$	334.094	+	89.5202i	0.0315717	+	0.00845962i
$483$	390.545	+	4119.23i	0.0367917	+	0.388057i
$484$	−5111.77	−	2951.28i	−0.480069	−	0.277168i
$485$	14425.0	+	4287.73i	1.35053	+	0.401435i
$486$	−381.505	−	422.514i	−0.0356078	−	0.0394354i
$487$	5958.98	+	5958.98i	0.554471	+	0.554471i	0.927728	−	0.373257i	$-0.121759\pi$
$487$	5958.98	+	5958.98i	0.554471	+	0.554471i	−0.373257	+	0.927728i	$0.621759\pi$
$488$	−2034.06	+	545.024i	−0.188683	+	0.0505575i
$489$	657.193	−	794.862i	0.0607756	−	0.0735070i
$490$	−9.28459	−	38.8349i	−0.000855990	−	0.00358037i
$491$	1593.20	−	919.833i	0.146436	−	0.0845447i	−0.424992	−	0.905197i	$-0.639723\pi$
$491$	1593.20	−	919.833i	0.146436	−	0.0845447i	0.571428	+	0.820652i	$0.306390\pi$
$492$	653.091	−	1427.53i	0.0598448	−	0.130809i
$493$	−4317.64	−	16113.7i	−0.394436	−	1.47205i
$494$	−339.202			−0.0308936
$495$	4646.28	+	5681.12i	0.421889	+	0.515854i
$496$	−15648.9			−1.41665
$497$	2470.86	+	9221.36i	0.223004	+	0.832263i
$498$	27.6313	+	38.8580i	0.00248633	+	0.00349653i
$499$	16091.2	−	9290.24i	1.44357	−	0.833443i	0.445480	−	0.895292i	$-0.353033\pi$
$499$	16091.2	−	9290.24i	1.44357	−	0.833443i	0.998086	+	0.0618488i	$0.0196996\pi$
$500$	4771.10	+	10076.3i	0.426740	+	0.901252i
$501$	6211.11	+	1048.74i	0.553876	+	0.0935218i
$502$	−272.306	+	72.9642i	−0.0242104	+	0.00648715i
$503$	−13205.7	−	13205.7i	−1.17060	−	1.17060i	−0.982066	−	0.188537i	$-0.939625\pi$
$503$	−13205.7	−	13205.7i	−1.17060	−	1.17060i	−0.188537	−	0.982066i	$-0.560375\pi$
$504$	1094.11	+	380.323i	0.0966976	+	0.0336130i
$505$	9623.31	+	17764.0i	0.847984	+	1.56532i
$506$	141.022	+	81.4188i	0.0123897	+	0.00715318i
$507$	−3108.98	−	1422.35i	−0.272337	−	0.124593i
$508$	5838.18	+	1564.34i	0.509897	+	0.136626i
$509$	−5734.05	−	9931.67i	−0.499327	−	0.864860i	0.500673	−	0.865637i	$-0.333086\pi$
$509$	−5734.05	−	9931.67i	−0.499327	−	0.864860i	−1.00000		0.000776870i	$0.999753\pi$
$510$	430.898	+	642.167i	0.0374127	+	0.0557562i
$511$	7323.15	−	12684.1i	0.633967	−	1.09806i
$512$	2151.81	−	2151.81i	0.185737	−	0.185737i
$513$	1658.21	+	5689.78i	0.142713	+	0.489688i
$514$			680.132i			0.0583645i
$515$	3340.70	+	3527.04i	0.285843	+	0.301786i
$516$	−4340.01	−	3588.32i	−0.370268	−	0.306138i
$517$	1735.91	−	6478.52i	0.147670	−	0.551112i
$518$	−125.697	+	469.108i	−0.0106618	+	0.0397904i
$519$	−2838.49	+	1056.53i	−0.240069	+	0.0893573i
$520$	38.9041	−	1433.86i	0.00328088	−	0.120921i
$521$			6391.36i			0.537449i	0.963217	+	0.268724i	$0.0866021\pi$
$521$			6391.36i			0.537449i	−0.963217	+	0.268724i	$0.913398\pi$
$522$	−762.155	−	55.5404i	−0.0639054	−	0.00465697i
$523$	−1085.21	+	1085.21i	−0.0907319	+	0.0907319i	−0.751016	−	0.660284i	$-0.770436\pi$
$523$	−1085.21	+	1085.21i	−0.0907319	+	0.0907319i	0.660284	+	0.751016i	$0.270436\pi$
$524$	−5368.97	+	9299.32i	−0.447604	+	0.775273i
$525$	−8529.78	−	7868.94i	−0.709086	−	0.654150i
$526$	430.879	+	746.304i	0.0357171	+	0.0618639i
$527$	21099.1	+	5653.50i	1.74401	+	0.467306i
$528$	−6533.38	+	4645.78i	−0.538502	+	0.382920i
$529$	8816.75	+	5090.35i	0.724644	+	0.418374i
$530$	1064.20	−	576.510i	0.0872185	−	0.0472490i
$531$	−7716.64	−	8929.70i	−0.630647	−	0.729786i
$532$	−4257.50	−	4257.50i	−0.346966	−	0.346966i
$533$	1954.58	−	523.728i	0.158841	−	0.0425613i
$534$	233.922	+	628.460i	0.0189566	+	0.0509291i
$535$	12053.9	−	2881.83i	0.974086	−	0.232883i
$536$	−746.532	+	431.010i	−0.0601591	+	0.0347329i
$537$	−8179.82	+	775.530i	−0.657328	+	0.0623214i
$538$	268.866	+	1003.42i	0.0215458	+	0.0804100i
$539$	−577.774			−0.0461716
$540$	−12103.8	+	3174.00i	−0.964564	+	0.252939i
$541$	−5696.04			−0.452665			−0.226333	−	0.974050i	$-0.572674\pi$
$541$	−5696.04			−0.452665			−0.226333	+	0.974050i	$0.572674\pi$
$542$	224.323	+	837.184i	0.0177776	+	0.0663471i
$543$	9486.92	−	899.456i	0.749766	−	0.0710854i
$544$	−2205.10	+	1273.11i	−0.173792	+	0.100339i
$545$	2038.03	−	3318.72i	0.160183	−	0.260841i
$546$	260.054	+	698.665i	0.0203833	+	0.0547621i
$547$	9610.88	−	2575.23i	0.751246	−	0.201296i	0.137175	−	0.990547i	$-0.456198\pi$
$547$	9610.88	−	2575.23i	0.751246	−	0.201296i	0.614071	+	0.789251i	$0.289531\pi$
$548$	4321.61	+	4321.61i	0.336880	+	0.336880i
$549$	−7774.85	+	22366.6i	−0.604412	+	1.73877i
$550$	−446.911	+	94.1107i	−0.0346479	+	0.00729617i
$551$	6889.80	+	3977.83i	0.532696	+	0.307552i
$552$	−453.164	+	322.238i	−0.0349419	+	0.0248467i
$553$	10406.8	+	2788.50i	0.800258	+	0.214428i
$554$	248.446	+	430.322i	0.0190532	+	0.0330011i
$555$	−3396.98	−	9943.37i	−0.259809	−	0.760491i
$556$	3944.39	−	6831.88i	0.300862	−	0.521109i
$557$	2392.66	−	2392.66i	0.182011	−	0.182011i	−0.610220	−	0.792232i	$-0.708919\pi$
$557$	2392.66	−	2392.66i	0.182011	−	0.182011i	0.792232	+	0.610220i	$0.208919\pi$
$558$	561.962	−	827.898i	0.0426340	−	0.0628095i
$559$		−	7258.82i		−	0.549223i
$560$	9203.47	−	8717.24i	0.694496	−	0.657805i
$561$	10487.2	−	3903.50i	0.789253	−	0.293772i
$562$	−72.7463	+	271.493i	−0.00546018	+	0.0203777i
$563$	−262.709	+	980.442i	−0.0196658	+	0.0733938i	−0.975061	−	0.221935i	$-0.928763\pi$
$563$	−262.709	+	980.442i	−0.0196658	+	0.0733938i	0.955396	+	0.295329i	$0.0954293\pi$
$564$	8813.12	+	7286.69i	0.657977	+	0.544016i
$565$	3931.15	−	3723.47i	0.292717	−	0.277252i
$566$		−	371.677i		−	0.0276020i
$567$	10448.1	−	7777.62i	0.773863	−	0.576066i
$568$	−907.180	+	907.180i	−0.0670148	+	0.0670148i
$569$	−12362.1	+	21411.8i	−0.910801	+	1.57755i	−0.0978658	+	0.995200i	$0.531202\pi$
$569$	−12362.1	+	21411.8i	−0.910801	+	1.57755i	−0.812935	+	0.582354i	$0.802132\pi$
$570$	−361.857	−	71.2437i	−0.0265904	−	0.00523521i
$571$	−1037.16	−	1796.41i	−0.0760136	−	0.131659i	0.825513	−	0.564383i	$-0.190886\pi$
$571$	−1037.16	−	1796.41i	−0.0760136	−	0.131659i	−0.901527	+	0.432724i	$0.857553\pi$
$572$	−10010.0	−	2682.17i	−0.731711	−	0.196061i
$573$	20656.4	+	9450.24i	1.50599	+	0.688987i
$574$	−88.0645	−	50.8441i	−0.00640373	−	0.00369720i
$575$	5451.43	−	1147.96i	0.395374	−	0.0832581i
$576$	−2554.06	−	13348.2i	−0.184755	−	0.965585i
$577$	2394.83	+	2394.83i	0.172787	+	0.172787i	0.788203	−	0.615416i	$-0.211012\pi$
$577$	2394.83	+	2394.83i	0.172787	+	0.172787i	−0.615416	+	0.788203i	$0.711012\pi$
$578$	425.770	−	114.085i	0.0306396	−	0.00820987i
$579$	2868.70	+	484.378i	0.205905	+	0.0347669i
$580$	−8790.14	+	14313.8i	−0.629294	+	1.02474i
$581$	−944.800	+	545.481i	−0.0674646	+	0.0389507i
$582$	−609.109	−	856.592i	−0.0433821	−	0.0610084i
$583$	−4532.77	−	16916.5i	−0.322004	−	1.20173i
$584$	1968.27			0.139465
$585$	−13094.8	−	9417.25i	−0.925477	−	0.665565i
$586$	−629.978			−0.0444098
$587$	−5532.39	−	20647.1i	−0.389005	−	1.45179i	−0.831756	−	0.555142i	$-0.812664\pi$
$587$	−5532.39	−	20647.1i	−0.389005	−	1.45179i	0.442751	−	0.896645i	$-0.354003\pi$
$588$	409.823	−	895.792i	0.0287429	−	0.0628263i
$589$	−9021.47	+	5208.55i	−0.631109	+	0.364371i
$590$	714.300	−	170.774i	0.0498429	−	0.0119164i
$591$	−5729.73	+	6930.00i	−0.398798	+	0.482339i
$592$	11086.7	−	2970.66i	0.769695	−	0.206239i
$593$	4483.83	+	4483.83i	0.310504	+	0.310504i	0.845105	−	0.534601i	$-0.179538\pi$
$593$	4483.83	+	4483.83i	0.310504	+	0.310504i	−0.534601	+	0.845105i	$0.679538\pi$
$594$	−11.1652	−	512.478i	−0.000771237	−	0.0353994i
$595$	−15558.2	+	8428.35i	−1.07197	+	0.580721i
$596$	867.967	+	501.121i	0.0596532	+	0.0344408i
$597$	557.720	+	5882.49i	0.0382344	+	0.403274i
$598$	−345.678	−	92.6242i	−0.0236385	−	0.00633392i
$599$	−5803.64	−	10052.2i	−0.395877	−	0.685679i	0.597336	−	0.801991i	$-0.296226\pi$
$599$	−5803.64	−	10052.2i	−0.395877	−	0.685679i	−0.993213	+	0.116312i	$0.962893\pi$
$600$	342.662	−	1521.46i	0.0233152	−	0.103522i
$601$	−12194.4	+	21121.3i	−0.827651	+	1.43353i	0.0722250	+	0.997388i	$0.476990\pi$
$601$	−12194.4	+	21121.3i	−0.827651	+	1.43353i	−0.899876	+	0.436145i	$0.856343\pi$
$602$	−257.936	+	257.936i	−0.0174629	+	0.0174629i
$603$	−704.506	+	9667.61i	−0.0475783	+	0.652895i
$604$		−	9087.42i		−	0.612188i
$605$	224.368	−	8269.40i	0.0150774	−	0.555701i
$606$	234.935	−	1391.39i	0.0157485	−	0.0932693i
$607$	−2699.06	+	10073.0i	−0.180480	+	0.673561i	0.815073	+	0.579358i	$0.196697\pi$
$607$	−2699.06	+	10073.0i	−0.180480	+	0.673561i	−0.995553	+	0.0942026i	$0.969970\pi$
$608$	314.281	−	1172.91i	0.0209635	−	0.0782368i
$609$	2911.10	−	17240.8i	0.193701	−	1.14718i
$610$	−1013.32	−	1069.84i	−0.0672592	−	0.0710108i
$611$			14740.3i			0.975986i
$612$	−1386.66	+	19028.4i	−0.0915886	+	1.25683i
$613$	1708.61	−	1708.61i	0.112577	−	0.112577i	−0.648574	−	0.761151i	$-0.724634\pi$
$613$	1708.61	−	1708.61i	0.112577	−	0.112577i	0.761151	+	0.648574i	$0.224634\pi$
$614$	−193.859	+	335.774i	−0.0127419	+	0.0220696i
$615$	2195.12	−	148.180i	0.143928	−	0.00971575i
$616$	521.513	+	903.286i	0.0341109	+	0.0590819i
$617$	−12394.7	−	3321.15i	−0.808740	−	0.216701i	−0.169322	−	0.985561i	$-0.554158\pi$
$617$	−12394.7	−	3321.15i	−0.808740	−	0.216701i	−0.639418	+	0.768860i	$0.720824\pi$
$618$	−32.0260	−	337.791i	−0.00208459	−	0.0219870i
$619$	−19133.4	−	11046.7i	−1.24238	−	0.717291i	−0.272806	−	0.962069i	$-0.587952\pi$
$619$	−19133.4	−	11046.7i	−1.24238	−	0.717291i	−0.969579	+	0.244778i	$0.921285\pi$
$620$	−10476.5	−	19338.9i	−0.678625	−	1.25269i
$621$	136.194	+	6251.22i	0.00880074	+	0.403950i
$622$	275.993	+	275.993i	0.0177915	+	0.0177915i
$623$	−14820.5	+	3971.15i	−0.953086	+	0.255379i
$624$	11226.7	−	13578.5i	0.720239	−	0.871116i
$625$	−9231.90	+	12606.1i	−0.590841	+	0.806788i
$626$	−620.439	+	358.210i	−0.0396130	+	0.0228706i
$627$	−2220.15	+	4852.81i	−0.141410	+	0.309095i
$628$	3587.57	+	13389.0i	0.227961	+	0.850762i
$629$	−16021.2			−1.01559
$630$	130.679	+	799.947i	0.00826410	+	0.0505883i
$631$	−26420.6			−1.66686			−0.833429	−	0.552626i	$-0.813626\pi$
$631$	−26420.6			−1.66686			−0.833429	+	0.552626i	$0.813626\pi$
$632$	374.737	+	1398.54i	0.0235858	+	0.0880235i
$633$	−15361.5	−	21602.9i	−0.964555	−	1.35646i
$634$	663.946	−	383.329i	0.0415909	−	0.0240125i
$635$	1969.69	+	8238.66i	0.123094	+	0.514868i
$636$	29442.9	+	4971.42i	1.83567	+	0.309952i
$637$	1226.52	−	328.646i	0.0762897	−	0.0204418i
$638$	−486.566	−	486.566i	−0.0301933	−	0.0301933i
$639$	2711.18	+	14169.4i	0.167844	+	0.877204i
$640$	3275.18	+	973.523i	0.202286	+	0.0601279i
$641$	−1204.90	−	695.650i	−0.0742445	−	0.0428651i	0.462418	−	0.886662i	$-0.346982\pi$
$641$	−1204.90	−	695.650i	−0.0742445	−	0.0428651i	−0.536663	+	0.843797i	$0.680315\pi$
$642$	−787.160	−	360.124i	−0.0483906	−	0.0221386i
$643$	20626.8	+	5526.95i	1.26508	+	0.338976i	0.828142	−	0.560518i	$-0.189398\pi$
$643$	20626.8	+	5526.95i	1.26508	+	0.338976i	0.436933	+	0.899494i	$0.356065\pi$
$644$	−3176.21	−	5501.36i	−0.194348	−	0.336621i
$645$	1524.59	−	7743.63i	0.0930711	−	0.472721i
$646$	−281.161	+	486.985i	−0.0171240	+	0.0296597i
$647$	19452.0	−	19452.0i	1.18197	−	1.18197i	0.202743	−	0.979232i	$-0.435014\pi$
$647$	19452.0	−	19452.0i	1.18197	−	1.18197i	0.979232	−	0.202743i	$-0.0649856\pi$
$648$	1607.22	+	693.374i	0.0974348	+	0.0420344i
$649$		−	10627.2i		−	0.642762i
$650$	895.189	−	453.991i	0.0540188	−	0.0273954i
$651$	17644.6	+	14588.6i	1.06228	+	0.878298i
$652$	−409.815	+	1529.45i	−0.0246159	+	0.0918679i
$653$	2984.75	−	11139.2i	0.178870	−	0.667553i	−0.816990	−	0.576652i	$-0.804359\pi$
$653$	2984.75	−	11139.2i	0.178870	−	0.667553i	0.995860	−	0.0909007i	$-0.0289746\pi$
$654$	−254.926	+	94.8874i	−0.0152422	+	0.00567338i
$655$	−15043.7	−	408.170i	−0.897412	−	0.0243489i
$656$			2403.25i			0.143035i
$657$	12430.2	−	18312.6i	0.738127	−	1.08743i
$658$	523.783	−	523.783i	0.0310322	−	0.0310322i
$659$	598.408	−	1036.47i	0.0353728	−	0.0612675i	−0.847797	−	0.530321i	$-0.822071\pi$
$659$	598.408	−	1036.47i	0.0353728	−	0.0612675i	0.883170	+	0.469053i	$0.155405\pi$
$660$	−10115.2	−	4963.73i	−0.596565	−	0.292747i
$661$	9399.91	+	16281.1i	0.553123	+	0.958037i	0.998047	+	0.0624685i	$0.0198973\pi$
$661$	9399.91	+	16281.1i	0.553123	+	0.958037i	−0.444924	+	0.895568i	$0.646769\pi$
$662$	−639.078	−	171.241i	−0.0375204	−	0.0100536i
$663$	−20042.3	+	14251.8i	−1.17403	+	0.834832i
$664$	−126.969	−	73.3055i	−0.00742070	−	0.00428434i
$665$	2404.30	−	8088.68i	0.140203	−	0.471678i
$666$	−240.968	+	693.213i	−0.0140200	+	0.0403325i
$667$	5935.14	+	5935.14i	0.344542	+	0.344542i
$668$	−9341.10	+	2502.94i	−0.541045	+	0.144973i
$669$	6075.64	+	16322.9i	0.351118	+	0.943319i
$670$	−514.020	−	315.661i	−0.0296393	−	0.0182016i
$671$	−18465.6	+	10661.1i	−1.06238	+	0.613366i
$672$	−2656.84	+	251.895i	−0.152514	+	0.0144599i
$673$	3866.49	+	14429.9i	0.221459	+	0.826498i	0.983792	+	0.179312i	$0.0573873\pi$
$673$	3866.49	+	14429.9i	0.221459	+	0.826498i	−0.762333	+	0.647185i	$0.775946\pi$
$674$	816.695			0.0466735
$675$	−11991.5	−	12796.6i	−0.683780	−	0.729688i
$676$	5248.88			0.298639
$677$	−5894.90	−	22000.1i	−0.334652	−	1.24894i	−0.904246	−	0.427012i	$-0.859566\pi$
$677$	−5894.90	−	22000.1i	−0.334652	−	1.24894i	0.569594	−	0.821926i	$-0.307100\pi$
$678$	−376.494	+	35.6954i	−0.0213262	+	0.00202194i
$679$	20827.3	−	12024.6i	1.17714	−	0.679622i
$680$	−2026.32	−	1244.37i	−0.114273	−	0.0701755i
$681$	−8219.22	−	22081.9i	−0.462498	−	1.24256i
$682$	870.304	−	233.197i	0.0488646	−	0.0130932i
$683$	−1310.24	−	1310.24i	−0.0734043	−	0.0734043i	0.669452	−	0.742856i	$-0.266529\pi$
$683$	−1310.24	−	1310.24i	−0.0734043	−	0.0734043i	−0.742856	+	0.669452i	$0.766529\pi$
$684$	−5949.11	−	6884.32i	−0.332559	−	0.384837i
$685$	−2440.51	+	8210.49i	−0.136127	+	0.457966i
$686$	−852.863	−	492.401i	−0.0474672	−	0.0274052i
$687$	788.736	−	560.858i	0.0438023	−	0.0311471i
$688$	8327.20	+	2231.27i	0.461441	+	0.123643i
$689$	19244.7	+	33332.8i	1.06410	+	1.84307i
$690$	−349.311	−	171.414i	−0.0192725	−	0.00945744i
$691$	2979.06	−	5159.89i	0.164007	−	0.284068i	−0.772295	−	0.635264i	$-0.780891\pi$
$691$	2979.06	−	5159.89i	0.164007	−	0.284068i	0.936302	+	0.351195i	$0.114225\pi$
$692$	3287.97	−	3287.97i	0.180621	−	0.180621i
$693$	11697.6	+	852.436i	0.641204	+	0.0467264i
$694$		−	1096.74i		−	0.0599879i
$695$	11052.0	+	299.868i	0.603206	+	0.0163664i
$696$	2202.13	−	819.667i	0.119930	−	0.0446399i
$697$	868.224	−	3240.26i	0.0471827	−	0.176088i
$698$	−51.3633	+	191.691i	−0.00278529	+	0.0103948i
$699$	−2123.24	−	1755.50i	−0.114890	−	0.0949915i
$700$	16934.3	+	5537.71i	0.914364	+	0.299008i
$701$			9865.95i			0.531572i	0.964032	+	0.265786i	$0.0856314\pi$
$701$			9865.95i			0.531572i	−0.964032	+	0.265786i	$0.914369\pi$
$702$	315.206	+	1081.56i	0.0169469	+	0.0581493i
$703$	5402.62	−	5402.62i	0.289849	−	0.289849i
$704$	6118.79	−	10598.0i	0.327572	−	0.567371i
$705$	−3095.95	+	15724.7i	−0.165390	+	0.840040i
$706$	503.662	+	872.368i	0.0268493	+	0.0465043i
$707$	31186.3	+	8356.33i	1.65895	+	0.444515i
$708$	16476.6	+	7537.98i	0.874614	+	0.400134i
$709$	−14785.0	−	8536.11i	−0.783161	−	0.452158i	0.0543884	−	0.998520i	$-0.482679\pi$
$709$	−14785.0	−	8536.11i	−0.783161	−	0.452158i	−0.837549	+	0.546362i	$0.816012\pi$
$710$	−860.541	−	255.789i	−0.0454867	−	0.0135206i
$711$	15378.4	+	5345.68i	0.811161	+	0.281967i
$712$	−1458.02	−	1458.02i	−0.0767436	−	0.0767436i
$713$	−10616.0	+	2844.54i	−0.557604	+	0.149410i
$714$	1218.61	+	205.762i	0.0638731	+	0.0107850i
$715$	−3377.17	−	14125.8i	−0.176642	−	0.738845i
$716$	10924.4	−	6307.21i	0.570201	−	0.329206i
$717$	17328.7	+	24369.4i	0.902584	+	1.26931i
$718$	−80.4333	−	300.181i	−0.00418070	−	0.0156026i
$719$	−2133.83			−0.110679			−0.0553397	−	0.998468i	$-0.517624\pi$
$719$	−2133.83			−0.110679			−0.0553397	+	0.998468i	$0.517624\pi$
$720$	14828.5	−	12127.4i	0.767535	−	0.627725i
$721$	7763.53			0.401011
$722$	197.378	+	736.626i	0.0101740	+	0.0379701i
$723$	−4975.33	+	10875.1i	−0.255926	+	0.559404i
$724$	−12670.1	+	7315.08i	−0.650387	+	0.375501i
$725$	−23506.8	−	1276.53i	−1.20417	−	0.0653919i
$726$	−368.170	+	445.294i	−0.0188210	+	0.0227637i
$727$	−11172.5	+	2993.67i	−0.569967	+	0.152722i	−0.532282	−	0.846567i	$-0.678665\pi$
$727$	−11172.5	+	2993.67i	−0.569967	+	0.152722i	−0.0376858	+	0.999290i	$0.511999\pi$
$728$	−1620.89	−	1620.89i	−0.0825195	−	0.0825195i
$729$	16601.2	−	10574.6i	0.843427	−	0.537243i
$730$	656.053	+	1211.03i	0.0332625	+	0.0614002i
$731$	−10421.3	−	6016.76i	−0.527287	−	0.304429i
$732$	−3431.33	−	36191.6i	−0.173259	−	1.82743i
$733$	−19973.5	−	5351.89i	−1.00647	−	0.269682i	−0.282314	−	0.959322i	$-0.591102\pi$
$733$	−19973.5	−	5351.89i	−1.00647	−	0.269682i	−0.724152	+	0.689640i	$0.757769\pi$
$734$	−245.249	−	424.783i	−0.0123328	−	0.0213611i
$735$	1377.47	−	92.9846i	0.0691273	−	0.00466638i
$736$	640.564	−	1109.49i	0.0320808	−	0.0555656i
$737$	−6171.88	+	6171.88i	−0.308472	+	0.308472i
$738$	−127.143	−	86.3021i	−0.00634172	−	0.00430464i
$739$			33141.9i			1.64972i	0.565336	+	0.824861i	$0.308747\pi$
$739$			33141.9i			1.64972i	−0.565336	+	0.824861i	$0.691253\pi$
$740$	11093.4	+	11712.1i	0.551082	+	0.581820i
$741$	1952.68	−	11564.6i	0.0968061	−	0.573328i
$742$	500.608	−	1868.30i	0.0247681	−	0.0924357i
$743$	3526.03	−	13159.3i	0.174101	−	0.649756i	−0.822601	−	0.568618i	$-0.807478\pi$
$743$	3526.03	−	13159.3i	0.174101	−	0.649756i	0.996703	−	0.0811372i	$-0.0258552\pi$
$744$	−512.253	+	3033.78i	−0.0252421	+	0.149494i
$745$	−38.0971	+	1404.12i	−0.00187352	+	0.0690512i
$746$		−	1024.58i		−	0.0502850i
$747$	−1483.87	+	718.356i	−0.0726801	+	0.0351851i
$748$	−12147.9	+	12147.9i	−0.593811	+	0.593811i
$749$	9903.04	−	17152.6i	0.483110	−	0.836771i
$750$	1050.33	−	296.292i	0.0511368	−	0.0144254i
$751$	−11601.2	−	20093.9i	−0.563694	−	0.976347i	−0.997170	−	0.0751815i	$-0.976046\pi$
$751$	−11601.2	−	20093.9i	−0.563694	−	0.976347i	0.433476	−	0.901165i	$-0.357287\pi$
$752$	−16909.8	−	4530.97i	−0.819996	−	0.219717i
$753$	−920.028	−	9703.90i	−0.0445255	−	0.469628i
$754$	1309.67	+	756.137i	0.0632563	+	0.0365210i
$755$	11198.4	−	6066.51i	0.539802	−	0.292428i
$756$	−9618.88	+	17531.5i	−0.462745	+	0.843407i
$757$	4639.72	+	4639.72i	0.222766	+	0.222766i	0.809662	−	0.586896i	$-0.199650\pi$
$757$	4639.72	+	4639.72i	0.222766	+	0.222766i	−0.586896	+	0.809662i	$0.699650\pi$
$758$	114.645	−	30.7190i	0.00549352	−	0.00147198i
$759$	−3587.67	+	4339.22i	−0.171573	+	0.207515i
$760$	1102.93	−	263.688i	0.0526416	−	0.0125855i
$761$	9261.02	−	5346.85i	0.441146	−	0.254696i	−0.262938	−	0.964813i	$-0.584691\pi$
$761$	9261.02	−	5346.85i	0.441146	−	0.254696i	0.704083	+	0.710117i	$0.251358\pi$
$762$	246.139	−	538.012i	0.0117017	−	0.0255776i
$763$	−1610.84	−	6011.75i	−0.0764305	−	0.285243i
$764$	−34874.0			−1.65144
$765$	−24374.3	+	10994.1i	−1.15197	+	0.519597i
$766$	−1910.64			−0.0901232
$767$	6044.87	+	22559.8i	0.284573	+	1.06204i
$768$	11987.2	+	16857.7i	0.563218	+	0.792056i
$769$	−7741.58	+	4469.60i	−0.363028	+	0.209594i	−0.670408	−	0.741993i	$-0.733881\pi$
$769$	−7741.58	+	4469.60i	−0.363028	+	0.209594i	0.307380	+	0.951587i	$0.400548\pi$
$770$	−381.942	+	621.952i	−0.0178756	+	0.0291086i
$771$	−23188.1	−	3915.30i	−1.08314	−	0.182887i
$772$	−4314.32	+	1156.02i	−0.201135	+	0.0538939i
$773$	25558.7	+	25558.7i	1.18924	+	1.18924i	0.977278	+	0.211961i	$0.0679849\pi$
$773$	25558.7	+	25558.7i	1.18924	+	1.18924i	0.211961	+	0.977278i	$0.432015\pi$
$774$	−417.079	+	360.421i	−0.0193690	+	0.0167378i
$775$	16837.4	−	25820.3i	0.780410	−	1.19676i
$776$	2798.92	+	1615.95i	0.129478	+	0.0747544i
$777$	−15269.9	−	6985.96i	−0.705027	−	0.322548i
$778$	−867.590	−	232.470i	−0.0399802	−	0.0107127i
$779$	799.891	+	1385.45i	0.0367896	+	0.0637214i
$780$	24296.4	+	4783.56i	1.11532	+	0.219588i
$781$	−6495.20	+	11250.0i	−0.297589	+	0.515439i
$782$	−419.507	+	419.507i	−0.0191836	+	0.0191836i
$783$	6281.05	−	25664.8i	0.286675	−	1.17137i
$784$			1508.07i			0.0686984i
$785$	−14104.2	+	13359.0i	−0.641274	+	0.607395i
$786$	810.078	+	669.773i	0.0367615	+	0.0303944i
$787$	6298.94	−	23508.0i	0.285303	−	1.06476i	−0.663315	−	0.748340i	$-0.730851\pi$
$787$	6298.94	−	23508.0i	0.285303	−	1.06476i	0.948618	−	0.316424i	$-0.102482\pi$
$788$	3572.97	−	13334.5i	0.161525	−	0.602820i
$789$	−27924.5	+	10393.9i	−1.26000	+	0.468991i
$790$	−735.581	+	696.720i	−0.0331276	+	0.0313774i
$791$		−	8653.05i		−	0.388959i
$792$	686.792	+	1418.67i	0.0308133	+	0.0636494i
$793$	33135.4	−	33135.4i	1.48382	−	1.48382i
$794$	439.543	−	761.312i	0.0196459	−	0.0340276i
$795$	13529.0	+	39601.0i	0.603553	+	1.76667i
$796$	−4535.81	−	7856.25i	−0.201969	−	0.349821i
$797$	−12639.4	−	3386.73i	−0.561746	−	0.150520i	−0.0332379	−	0.999447i	$-0.510582\pi$
$797$	−12639.4	−	3386.73i	−0.561746	−	0.150520i	−0.528509	+	0.848928i	$0.677249\pi$
$798$	−480.324	+	341.551i	−0.0213074	+	0.0151514i
$799$	21162.3	+	12218.0i	0.937005	+	0.540980i
$800$	740.417	+	3516.08i	0.0327221	+	0.155390i
$801$	−22773.0	+	4357.39i	−1.00455	+	0.192211i
$802$	334.321	+	334.321i	0.0147198	+	0.0147198i
$803$	19250.5	−	5158.17i	0.845999	−	0.226685i
$804$	−5191.21	−	13946.8i	−0.227711	−	0.611773i
$805$	4658.94	−	7586.59i	0.203983	−	0.332164i
$806$	−1714.87	+	990.081i	−0.0749426	+	0.0432681i
$807$	−35758.0	+	3390.22i	−1.55978	+	0.147883i
$808$	1122.98	+	4191.02i	0.0488940	+	0.182475i
$809$	6305.31			0.274021			0.137010	−	0.990570i	$-0.456251\pi$
$809$	6305.31			0.274021			0.137010	+	0.990570i	$0.456251\pi$
$810$	109.095	+	1220.00i	0.00473236	+	0.0529214i
$811$	17097.2			0.740277			0.370139	−	0.928976i	$-0.379310\pi$
$811$	17097.2			0.740277			0.370139	+	0.928976i	$0.379310\pi$
$812$	6947.65	+	25929.0i	0.300264	+	1.12060i
$813$	−29833.9	+	2828.55i	−1.28699	+	0.122019i
$814$	−572.310	+	330.423i	−0.0246430	+	0.0142277i
$815$	−2158.31	+	516.007i	−0.0927637	+	0.0221778i
$816$	−10188.7	−	27373.1i	−0.437101	−	1.17432i
$817$	5543.21	−	1485.30i	0.237371	−	0.0636035i
$818$	685.967	+	685.967i	0.0293206	+	0.0293206i
$819$	−25317.0	+	4844.16i	−1.08015	+	0.206677i
$820$	−2969.94	+	1608.91i	−0.126481	+	0.0685190i
$821$	24722.6	+	14273.6i	1.05095	+	0.606764i	0.922914	−	0.385006i	$-0.125801\pi$
$821$	24722.6	+	14273.6i	1.05095	+	0.606764i	0.128032	+	0.991770i	$0.459134\pi$
$822$	487.558	−	346.694i	0.0206880	−	0.0147109i
$823$	−22523.4	−	6035.14i	−0.953970	−	0.255616i	−0.251924	−	0.967747i	$-0.581063\pi$
$823$	−22523.4	−	6035.14i	−0.953970	−	0.255616i	−0.702046	+	0.712131i	$0.747730\pi$
$824$	521.658	+	903.539i	0.0220544	+	0.0381994i
$825$	−635.844	−	15778.5i	−0.0268330	−	0.665864i
$826$	586.842	−	1016.44i	0.0247202	−	0.0428166i
$827$	−27708.7	+	27708.7i	−1.16509	+	1.16509i	−0.181739	+	0.983347i	$0.558173\pi$
$827$	−27708.7	+	27708.7i	−1.16509	+	1.16509i	−0.983347	+	0.181739i	$0.941827\pi$
$828$	−4182.83	−	8640.26i	−0.175560	−	0.362645i
$829$		−	31698.4i		−	1.32802i	−0.747722	−	0.664012i	$-0.768853\pi$
$829$		−	31698.4i		−	1.32802i	0.747722	−	0.664012i	$-0.231147\pi$
$830$	2.78254	−	102.555i	0.000116366	−	0.00428882i
$831$	−16101.4	+	5993.19i	−0.672144	+	0.250182i
$832$	−6960.89	+	25978.4i	−0.290055	+	1.08250i
$833$	544.821	−	2033.30i	0.0226614	−	0.0845734i
$834$	−595.135	−	492.058i	−0.0247097	−	0.0204300i
$835$	−9320.21	−	9840.08i	−0.386275	−	0.407820i
$836$		−	8192.97i		−	0.338947i
$837$	24990.9	+	23925.2i	1.03203	+	0.988024i
$838$	506.289	−	506.289i	0.0208705	−	0.0208705i
$839$	5091.06	−	8817.98i	0.209491	−	0.362849i	−0.742063	−	0.670330i	$-0.766153\pi$
$839$	5091.06	−	8817.98i	0.209491	−	0.362849i	0.951554	+	0.307481i	$0.0994860\pi$
$840$	−1388.70	−	2069.59i	−0.0570415	−	0.0850089i
$841$	−5539.95	−	9595.47i	−0.227149	−	0.393434i
$842$	−601.821	−	161.258i	−0.0246320	−	0.00660012i
$843$	−8837.38	−	4043.08i	−0.361062	−	0.165185i
$844$	35243.8	+	20348.0i	1.43737	+	0.829867i
$845$	3504.00	+	6468.15i	0.142653	+	0.263327i
$846$	846.950	−	731.895i	0.0344193	−	0.0297436i
$847$	−9348.01	−	9348.01i	−0.379222	−	0.379222i
$848$	−44154.4	+	11831.1i	−1.78805	+	0.479107i
$849$	12671.8	+	2139.62i	0.512243	+	0.0864919i
$850$	90.2277	−	1661.51i	0.00364092	−	0.0670463i
$851$	6981.04	−	4030.51i	0.281207	−	0.162355i
$852$	−12835.1	−	18050.1i	−0.516108	−	0.725805i
$853$	−1220.90	−	4556.47i	−0.0490069	−	0.182896i	0.937084	−	0.349105i	$-0.113514\pi$
$853$	−1220.90	−	4556.47i	−0.0490069	−	0.182896i	−0.986091	+	0.166208i	$0.946848\pi$
$854$	−2354.88			−0.0943586
$855$	4512.04	−	11926.8i	0.180478	−	0.477063i
$856$	2661.68			0.106278
$857$	−157.438	−	587.566i	−0.00627535	−	0.0234199i	0.962717	−	0.270510i	$-0.0871923\pi$
$857$	−157.438	−	587.566i	−0.00627535	−	0.0234199i	−0.968993	+	0.247090i	$0.920526\pi$
$858$	−422.023	+	922.460i	−0.0167921	+	0.0367043i
$859$	6676.93	−	3854.93i	0.265208	−	0.153118i	−0.361500	−	0.932372i	$-0.617735\pi$
$859$	6676.93	−	3854.93i	0.265208	−	0.153118i	0.626708	+	0.779254i	$0.284402\pi$
$860$	2817.43	+	11784.5i	0.111714	+	0.467267i
$861$	2240.41	−	2709.74i	0.0886795	−	0.107256i
$862$	1321.93	−	354.210i	0.0522333	−	0.0139959i
$863$	12354.8	+	12354.8i	0.487326	+	0.487326i	0.907461	−	0.420135i	$-0.138017\pi$
$863$	12354.8	+	12354.8i	0.487326	+	0.487326i	−0.420135	+	0.907461i	$0.638017\pi$
$864$	−4031.93	+	87.8425i	−0.158760	+	0.00345887i
$865$	6246.69	+	1856.78i	0.245542	+	0.0729856i
$866$	−220.090	−	127.069i	−0.00863623	−	0.00498613i
$867$	1438.53	+	15172.8i	0.0563495	+	0.594341i
$868$	−33951.3	−	9097.21i	−1.32763	−	0.355737i
$869$	7330.19	+	12696.3i	0.286145	+	0.495617i
$870$	1238.32	+	1081.71i	0.0482564	+	0.0421534i
$871$	9591.27	−	16612.6i	0.373120	−	0.646263i
$872$	591.424	−	591.424i	0.0229681	−	0.0229681i
$873$	32710.7	−	15835.5i	1.26814	−	0.613920i
$874$		−	282.931i		−	0.0109500i
$875$	4480.77	+	24564.8i	0.173117	+	0.949076i
$876$	−5657.34	+	33505.2i	−0.218201	+	1.29228i
$877$	3022.83	−	11281.4i	0.116390	−	0.434372i	−0.882998	−	0.469378i	$-0.844478\pi$
$877$	3022.83	−	11281.4i	0.116390	−	0.434372i	0.999387	+	0.0350058i	$0.0111450\pi$
$878$	−78.8563	+	294.296i	−0.00303106	+	0.0113121i
$879$	3626.58	−	21478.2i	0.139160	−	0.824165i
$880$	17243.0	+	467.841i	0.660523	+	0.0179215i
$881$		−	47696.1i		−	1.82398i	−0.410216	−	0.911989i	$-0.634547\pi$
$881$		−	47696.1i		−	1.82398i	0.410216	−	0.911989i	$-0.365453\pi$
$882$	−79.7836	−	54.1556i	−0.00304586	−	0.00206748i
$883$	−35945.1	+	35945.1i	−1.36993	+	1.36993i	−0.509398	+	0.860531i	$0.670132\pi$
$883$	−35945.1	+	35945.1i	−1.36993	+	1.36993i	−0.860531	+	0.509398i	$0.829868\pi$
$884$	18878.2	−	32697.9i	0.718259	−	1.24406i
$885$	1710.29	+	25336.1i	0.0649614	+	0.962332i
$886$	−74.2205	−	128.554i	−0.00281432	−	0.00487455i
$887$	18701.8	+	5011.14i	0.707943	+	0.189693i	0.594786	−	0.803884i	$-0.297237\pi$
$887$	18701.8	+	5011.14i	0.707943	+	0.189693i	0.113158	+	0.993577i	$0.463904\pi$
$888$	−212.997	−	2246.56i	−0.00804922	−	0.0848983i
$889$	11723.5	+	6768.57i	0.442288	+	0.255355i
$890$	411.104	−	1383.06i	0.0154834	−	0.0520902i
$891$	17536.5	+	2569.51i	0.659364	+	0.0966126i
$892$	−18907.7	−	18907.7i	−0.709726	−	0.709726i
$893$	−11256.4	+	3016.15i	−0.421816	+	0.113025i
$894$	62.5143	−	75.6099i	0.00233869	−	0.00282861i
$895$	15065.2	+	9251.55i	0.562651	+	0.345525i
$896$	4728.80	−	2730.18i	0.176315	−	0.101795i
$897$	5147.84	−	11252.2i	0.191618	−	0.418840i
$898$	−392.767	−	1465.83i	−0.0145955	−	0.0544713i
$899$	46442.8			1.72297
$900$	24914.4	+	10206.1i	0.922754	+	0.378003i
$901$	63806.8			2.35928
$902$	−35.8128	−	133.655i	−0.00132199	−	0.00493373i
$903$	−7309.09	−	10278.8i	−0.269359	−	0.378801i
$904$	1007.06	−	581.428i	0.0370513	−	0.0213916i
$905$	−17472.5	−	10729.9i	−0.641775	−	0.394115i
$906$	−877.126	−	148.102i	−0.0321640	−	0.00543087i
$907$	−27962.8	+	7492.61i	−1.02369	+	0.274298i	−0.731340	−	0.682013i	$-0.761105\pi$
$907$	−27962.8	+	7492.61i	−1.02369	+	0.274298i	−0.292353	+	0.956311i	$0.594438\pi$
$908$	25578.6	+	25578.6i	0.934863	+	0.934863i
$909$	46084.8	+	16019.5i	1.68156	+	0.584525i
$910$	457.028	−	1537.56i	0.0166487	−	0.0560106i
$911$	5199.96	+	3002.20i	0.189113	+	0.109185i	0.591567	−	0.806256i	$-0.298509\pi$
$911$	5199.96	+	3002.20i	0.189113	+	0.109185i	−0.402454	+	0.915440i	$0.631843\pi$
$912$	12666.5	+	5794.88i	0.459900	+	0.210403i
$913$	−1433.92	−	384.217i	−0.0519779	−	0.0139274i
$914$	−816.525	−	1414.26i	−0.0295495	−	0.0511812i
$915$	42308.0	−	28388.9i	1.52859	−	1.02569i
$916$	−742.921	+	1286.78i	−0.0267978	+	0.0464152i
$917$	−17005.9	+	17005.9i	−0.612414	+	0.612414i
$918$	1814.04	+	443.957i	0.0652203	+	0.0159616i
$919$			24904.8i			0.893942i	0.894548	+	0.446971i	$0.147497\pi$
$919$			24904.8i			0.893942i	−0.894548	+	0.446971i	$0.852503\pi$
$920$	1196.00	+	32.4501i	0.0428596	+	0.00116288i
$921$	−10331.7	−	8542.28i	−0.369644	−	0.305622i
$922$	−733.129	+	2736.07i	−0.0261869	+	0.0977308i
$923$	7389.12	−	27576.6i	0.263506	−	0.983417i
$924$	−16875.3	+	6281.24i	−0.600819	+	0.223634i
$925$	−7027.16	+	21489.0i	−0.249786	+	0.763842i
$926$		−	146.542i		−	0.00520050i
$927$	11700.9	+	852.675i	0.414570	+	0.0302109i
$928$	−3828.06	+	3828.06i	−0.135412	+	0.135412i
$929$	7683.25	−	13307.8i	0.271345	−	0.469983i	−0.697862	−	0.716232i	$-0.745865\pi$
$929$	7683.25	−	13307.8i	0.271345	−	0.469983i	0.969206	+	0.246250i	$0.0791984\pi$
$930$	−2037.35	+	696.026i	−0.0718360	+	0.0245415i
$931$	501.942	+	869.388i	0.0176697	+	0.0306048i
$932$	4085.48	+	1094.70i	0.143588	+	0.0384744i
$933$	−10998.4	+	7820.76i	−0.385927	+	0.274427i
$934$	−2234.71	−	1290.21i	−0.0782890	−	0.0452002i
$935$	−23079.4	−	6860.17i	−0.807247	−	0.239948i
$936$	−2264.91	−	2620.96i	−0.0790928	−	0.0915263i
$937$	19626.7	+	19626.7i	0.684286	+	0.684286i	0.960963	−	0.276677i	$-0.0892333\pi$
$937$	19626.7	+	19626.7i	0.684286	+	0.684286i	−0.276677	+	0.960963i	$0.589233\pi$
$938$	−931.131	+	249.496i	−0.0324120	+	0.00868478i
$939$	−8640.99	−	23215.0i	−0.300307	−	0.806810i
$940$	−5721.28	−	23930.5i	−0.198519	−	0.830348i
$941$	−33081.5	+	19099.6i	−1.14604	+	0.661668i	−0.947920	−	0.318509i	$-0.896818\pi$
$941$	−33081.5	+	19099.6i	−1.14604	+	0.661668i	−0.198123	+	0.980177i	$0.563484\pi$
$942$	1350.78	−	128.068i	0.0467207	−	0.00442960i
$943$	436.845	+	1630.33i	0.0150855	+	0.0562998i
$944$	−27738.3			−0.956361
$945$	−28025.3	−	149.723i	−0.964722	−	0.00515397i
$946$	−496.362			−0.0170593
$947$	−5283.39	−	19717.9i	−0.181296	−	0.676605i	−0.995393	−	0.0958767i	$-0.969435\pi$
$947$	−5283.39	−	19717.9i	−0.181296	−	0.676605i	0.814097	−	0.580728i	$-0.197232\pi$
$948$	−24883.9	+	2359.25i	−0.852524	+	0.0808279i
$949$	−37931.8	+	21899.9i	−1.29749	+	0.749106i
$950$	529.864	+	590.717i	0.0180959	+	0.0201741i
$951$	9246.92	+	24842.9i	0.315302	+	0.847095i
$952$	−3670.61	+	983.537i	−0.124963	+	0.0334838i
$953$	−16077.4	−	16077.4i	−0.546482	−	0.546482i	0.378939	−	0.925422i	$-0.376289\pi$
$953$	−16077.4	−	16077.4i	−0.546482	−	0.546482i	−0.925422	+	0.378939i	$0.876289\pi$
$954$	959.691	−	2760.83i	0.0325693	−	0.0936952i
$955$	−23280.9	−	42975.0i	−0.788852	−	1.45617i
$956$	−39757.3	−	22953.9i	−1.34502	−	0.776550i
$957$	19389.7	−	13787.7i	0.654944	−	0.465720i
$958$	2401.57	+	643.499i	0.0809929	+	0.0217020i
$959$	6844.23	+	11854.5i	0.230460	+	0.399169i
$960$	−12882.1	+	26251.4i	−0.433093	+	0.882564i
$961$	−15510.5	+	26864.9i	−0.520642	+	0.901779i
$962$	1026.97	−	1026.97i	0.0344188	−	0.0344188i
$963$	16809.3	−	24763.9i	0.562484	−	0.828668i
$964$		−	18360.4i		−	0.613431i
$965$	−4304.68	−	4544.79i	−0.143598	−	0.151608i
$966$	−582.761	+	216.912i	−0.0194100	+	0.00722468i
$967$	−2833.64	+	10575.3i	−0.0942335	+	0.351684i	−0.996902	−	0.0786521i	$-0.974938\pi$
$967$	−2833.64	+	10575.3i	−0.0942335	+	0.351684i	0.902669	+	0.430336i	$0.141605\pi$
$968$	459.819	−	1716.07i	0.0152677	−	0.0569799i
$969$	−14984.5	−	12389.2i	−0.496770	−	0.410730i
$970$	−61.3387	+	2260.73i	−0.00203038	+	0.0748325i
$971$		−	52152.6i		−	1.72364i	−0.507213	−	0.861821i	$-0.669324\pi$
$971$		−	52152.6i		−	1.72364i	0.507213	−	0.861821i	$-0.330676\pi$
$972$	−16422.7	+	25366.3i	−0.541931	+	0.837062i
$973$	12493.6	−	12493.6i	0.411641	−	0.411641i
$974$	−633.232	+	1096.79i	−0.0208317	+	0.0360815i
$975$	10324.8	+	33133.6i	0.339138	+	1.08833i
$976$	27827.0	+	48197.8i	0.912624	+	1.58071i
$977$	2355.06	+	631.037i	0.0771188	+	0.0206639i	0.297172	−	0.954824i	$-0.403956\pi$
$977$	2355.06	+	631.037i	0.0771188	+	0.0206639i	−0.220053	+	0.975488i	$0.570623\pi$
$978$	140.945	+	64.4819i	0.00460830	+	0.00210829i
$979$	−18081.0	−	10439.1i	−0.590267	−	0.340791i
$980$	−1863.67	+	1009.61i	−0.0607478	+	0.0329090i
$981$	−1767.52	−	9237.57i	−0.0575255	−	0.300645i
$982$	195.492	+	195.492i	0.00635276	+	0.00635276i
$983$	32201.1	−	8628.26i	1.04482	−	0.279958i	0.304709	−	0.952446i	$-0.401441\pi$
$983$	32201.1	−	8628.26i	1.04482	−	0.279958i	0.740108	+	0.672488i	$0.234774\pi$
$984$	465.907	+	78.6681i	0.0150941	+	0.00254863i
$985$	18817.2	−	4498.80i	0.608697	−	0.145527i
$986$	2171.14	−	1253.51i	0.0701248	−	0.0404866i
$987$	14842.3	+	20872.8i	0.478660	+	0.673141i
$988$	4660.27	+	17392.4i	0.150064	+	0.560045i
$989$	6054.63			0.194667
$990$	−643.956	+	895.430i	−0.0206730	+	0.0287461i
$991$	−25052.6			−0.803051			−0.401525	−	0.915848i	$-0.631520\pi$
$991$	−25052.6			−0.803051			−0.401525	+	0.915848i	$0.631520\pi$
$992$	−1834.68	−	6847.13i	−0.0587210	−	0.219150i
$993$	9517.16	−	20802.6i	0.304147	−	0.664806i
$994$	−1242.48	+	717.344i	−0.0396468	+	0.0228901i
$995$	6653.23	−	10834.1i	0.211981	−	0.345189i
$996$	1612.80	−	1950.65i	0.0513086	−	0.0620568i
$997$	−6552.85	+	1755.83i	−0.208155	+	0.0557750i	−0.361390	−	0.932415i	$-0.617698\pi$
$997$	−6552.85	+	1755.83i	−0.208155	+	0.0557750i	0.153235	+	0.988190i	$0.451031\pi$
$998$	1974.46	+	1974.46i	0.0626256	+	0.0626256i
$999$	−22246.9	−	12206.0i	−0.704565	−	0.386568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.2.9	✓	64
3.2	odd	2		135.4.m.a.62.8		64
5.2	odd	4		225.4.p.b.218.8		64
5.3	odd	4	inner	45.4.l.a.38.9	yes	64
5.4	even	2		225.4.p.b.182.8		64
9.4	even	3		135.4.m.a.17.8		64
9.5	odd	6	inner	45.4.l.a.32.9	yes	64
15.8	even	4		135.4.m.a.8.8		64
45.13	odd	12		135.4.m.a.98.8		64
45.14	odd	6		225.4.p.b.32.8		64
45.23	even	12	inner	45.4.l.a.23.9	yes	64
45.32	even	12		225.4.p.b.68.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.9	✓	64	1.1	even	1	trivial
45.4.l.a.23.9	yes	64	45.23	even	12	inner
45.4.l.a.32.9	yes	64	9.5	odd	6	inner
45.4.l.a.38.9	yes	64	5.3	odd	4	inner
135.4.m.a.8.8		64	15.8	even	4
135.4.m.a.17.8		64	9.4	even	3
135.4.m.a.62.8		64	3.2	odd	2
135.4.m.a.98.8		64	45.13	odd	12
225.4.p.b.32.8		64	45.14	odd	6
225.4.p.b.68.8		64	45.32	even	12
225.4.p.b.182.8		64	5.4	even	2
225.4.p.b.218.8		64	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0388957 + 0.145161i) q^{2} +(-5.17295 + 0.490448i) q^{3} +(6.90864 - 3.98871i) q^{4} +(9.52728 + 5.85072i) q^{5} +(-0.272400 - 0.731834i) q^{6} +(17.2584 - 4.62436i) q^{7} +(1.69784 + 1.69784i) q^{8} +(26.5189 - 5.07413i) q^{9} +O(q^{10})\)	\(q+(0.0388957 + 0.145161i) q^{2} +(-5.17295 + 0.490448i) q^{3} +(6.90864 - 3.98871i) q^{4} +(9.52728 + 5.85072i) q^{5} +(-0.272400 - 0.731834i) q^{6} +(17.2584 - 4.62436i) q^{7} +(1.69784 + 1.69784i) q^{8} +(26.5189 - 5.07413i) q^{9} +(-0.478726 + 1.61056i) q^{10} +(21.0551 + 12.1562i) q^{11} +(-33.7818 + 24.0217i) q^{12} +(-51.6112 - 13.8292i) q^{13} +(1.34255 + 2.32537i) q^{14} +(-52.1537 - 25.5929i) q^{15} +(31.7292 - 54.9567i) q^{16} +(-62.6342 + 62.6342i) q^{17} +(1.76804 + 3.65215i) q^{18} -42.2427i q^{19} +(89.1574 + 2.41905i) q^{20} +(-87.0087 + 32.3859i) q^{21} +(-0.945647 + 3.52920i) q^{22} +(11.5350 - 43.0493i) q^{23} +(-9.61557 - 7.95016i) q^{24} +(56.5380 + 111.483i) q^{25} -8.02983i q^{26} +(-134.693 + 39.2544i) q^{27} +(100.787 - 100.787i) q^{28} +(-94.1659 + 163.100i) q^{29} +(1.68653 - 8.56613i) q^{30} +(-123.300 - 213.562i) q^{31} +(27.7661 + 7.43989i) q^{32} +(-114.879 - 52.5569i) q^{33} +(-11.5282 - 6.65583i) q^{34} +(191.481 + 56.9163i) q^{35} +(162.971 - 140.832i) q^{36} +(127.895 + 127.895i) q^{37} +(6.13199 - 1.64306i) q^{38} +(273.765 + 46.2251i) q^{39} +(6.24221 + 26.1094i) q^{40} +(-32.7974 + 18.9356i) q^{41} +(-8.08544 - 11.3706i) q^{42} +(35.1611 + 131.223i) q^{43} +193.950 q^{44} +(282.340 + 106.812i) q^{45} +6.69773 q^{46} +(-71.4005 - 266.470i) q^{47} +(-137.181 + 299.850i) q^{48} +(-20.5808 + 11.8823i) q^{49} +(-13.9839 + 12.5433i) q^{50} +(293.285 - 354.723i) q^{51} +(-411.724 + 110.321i) q^{52} +(-509.361 - 509.361i) q^{53} +(-10.9372 - 18.0253i) q^{54} +(129.475 + 239.003i) q^{55} +(37.1534 + 21.4505i) q^{56} +(20.7179 + 218.520i) q^{57} +(-27.3384 - 7.32531i) q^{58} +(-218.555 - 378.548i) q^{59} +(-462.394 + 31.2135i) q^{60} +(-438.507 + 759.517i) q^{61} +(26.2051 - 26.2051i) q^{62} +(434.208 - 210.204i) q^{63} -503.348i q^{64} +(-410.804 - 433.718i) q^{65} +(3.16090 - 18.7202i) q^{66} +(-92.9184 + 346.776i) q^{67} +(-182.888 + 682.547i) q^{68} +(-38.5567 + 228.349i) q^{69} +(-0.814223 + 30.0093i) q^{70} +534.313i q^{71} +(53.6400 + 36.4099i) q^{72} +(579.639 - 579.639i) q^{73} +(-13.5907 + 23.5399i) q^{74} +(-347.145 - 548.967i) q^{75} +(-168.494 - 291.840i) q^{76} +(419.591 + 112.429i) q^{77} +(3.93822 + 41.5379i) q^{78} +(522.214 + 301.501i) q^{79} +(623.830 - 337.948i) q^{80} +(677.506 - 269.121i) q^{81} +(-4.02439 - 4.02439i) q^{82} +(-58.9790 + 15.8034i) q^{83} +(-471.934 + 570.795i) q^{84} +(-963.189 + 230.278i) q^{85} +(-17.6808 + 10.2080i) q^{86} +(407.124 - 889.893i) q^{87} +(15.1090 + 56.3875i) q^{88} -858.746 q^{89} +(-4.52311 + 45.1393i) q^{90} -954.676 q^{91} +(-92.0196 - 343.422i) q^{92} +(742.569 + 1044.28i) q^{93} +(35.9039 - 20.7291i) q^{94} +(247.151 - 402.458i) q^{95} +(-147.281 - 24.8684i) q^{96} +(1300.14 - 348.372i) q^{97} +(-2.52535 - 2.52535i) q^{98} +(620.041 + 215.532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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